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1. Forces for the Navier-Stokes equations and the Koch and Tataru theorem

Author: Gilles Lemarié-Rieusset, Pierre, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry (LaMME)
Subjects: parabolic Morrey spaces, 35Q30, mild solutions, mild solutions AMS classification : 35K55, Navier-Stokes equations, [MATH]Mathematics [math], critical spaces, parabolic Sobolev spaces, 76D05
Abstract: We consider the Cauchy problem for the incompressible Navier--Stokes equations on the whole space $\mathbb{R}^3$, with initial value $\vec u_0\in {\rm BMO}^{-1}$ (as in Koch and Tataru's theorem) and with force $\vec f=\Div \mathbb{F}$ where smallness of $\mathbb{F}$ ensures existence of a mild solution in absence of initial value. We study the interaction of the two solutions and discuss the existence of global solution for the complete problem (i.e. in presence of initial value and forcing term) under smallness assumptions. In particular, we discuss the interaction between Koch and Tataru solutions and Lei-Lin's solutions (in $L^2\mathcal{F}^{-1}L^1$) or solutions in the multiplier space $\mathcal{M}(\dot H^{1/2,1}_{t,x}\mapsto L^2_{t,x})$.
Published: 2022

2. SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions

Author: Monique Jeanblanc, Frédéric Vrins, Damiano Brigo, UCL - SSH/LIDAM/LFIN - Louvain Finance, UCL - SSH/LIDAM/CORE - Center for operations research and econometrics, Department of Mathematics [Imperial College London], Imperial College London, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université Catholique de Louvain = Catholic University of Louvain (UCL), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Université Catholique de Louvain (UCL), ANR 11-LABX-0019., Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, JEANBLANC, Monique, UCL - SSH/IMMAQ/CORE - Center for operations research and econometrics, and UCL - SSH/IMMAQ/LFIN-Louvain Finance
Subjects: Uniform Martingale Diffusions, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Pure mathematics, Uniformly distributed stochastic differential equation, [MATH] Mathematics [math], math.PR, 01 natural sciences, gales, 010104 statistics & probability, Stochastic differential equation, Mathematics::Probability, 0102 Applied Mathematics, 60J60 * Department of Mathematics, Mean Reverting Uniform Diffusion, Mean reverting uniform diffusion, Maximum entropy stochastic recovery rates, [MATH]Mathematics [math], Maximum Entropy, Stochastic Recovery Rates, Imperial College, Mathematics, Conic Martin-gales, peacock process, Applied Mathematics, Weak solution, Principle of maximum entropy, 0104 Statistics, 1502 Banking, Finance and Investment, Uniformly distributed Stochastic Differential Equation, Uniform SDE Sim-ulation, Conic section, Modeling and Simulation, ulation, Peacock Process, Martingale (probability theory), Statistics and Probability, uniformmly distributed diffusion, Uniformly distributed diffusion, Statistics & Probability, conic martingales, Uniform SDE Sim, Mathematical Finance and Stochastic Analysis groups, Uniform Martingale diffusions, Maximum Entropy Stochastic Correlation, Modelling and Simulation, Uniformly distributed Diffusion, Ergodic theory, Maximum entropy stochastic correlation, 0101 mathematics, 010102 general mathematics, Maximum Entropy Stochastic Recovery Rates, Regular polygon, AMS classification codes: 60H10, mean reverting uniform SDE, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 60H10, 60J60, Mean Reverting Uniform SDE, Local time, Conic Martin, Uniform SDE simulation
Abstract: It is known since Kellerer (1972) that for any peacock process there exist mar-tingales with the same marginal laws. Nevertheless, there is no general method for finding such martingales that yields diffusions. Indeed, Kellerer's proof is not constructive: finding the dynamics of processes associated to a given peacock is not trivial in general. In this paper we are interested in the uniform peacock that is, the peacock with uniform law at all times on a generic time-varying support [a(t), b(t)]. We derive explicitly the corresponding Stochastic Differential Equations (SDEs) and prove that, under certain conditions on the boundaries a(t) and b(t), they admit a unique strong solution yielding the relevant diffusion process. We discuss the relationship between our result and the previous derivation of diffusion processes associated to square-root and linear time-boundaries, emphasizing the cases where our approach adds strong uniqueness, and study the local time and activity of the solution processes. We then study the peacock with uniform law at all times on a constant support [−1, 1] and derive the SDE of an associated mean-reverting diffusion process with uniform margins that is not a martingale. For the related SDE we prove existence of a solution in [0, T ]. Finally, we provide a numerical case study showing that these processes have the desired uniform behaviour. These results may be used to model random probabilities, random recovery rates or random correlations.
Published: 2020
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3. Conic martingales from stochastic integrals

Author: Frédéric Vrins, Monique Jeanblanc, Université Catholique de Louvain (UCL), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), JEANBLANC, Monique, Université Catholique de Louvain = Catholic University of Louvain (UCL), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry
Subjects: [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Economics and Econometrics, Pure mathematics, [MATH] Mathematics [math], stochastic differential equation, 01 natural sciences, Separable space, Stochastic differential equation, 010104 statistics & probability, symbols.namesake, Mathematics::Probability, Wiener process, Accounting, 0502 economics and business, Applied mathematics, [MATH]Mathematics [math], 0101 mathematics, Martingale representation theorem, Brownian motion, Mathematics, Discrete mathematics, Geometric Brownian motion, 050208 finance, Stochastic process, Applied Mathematics, 010102 general mathematics, 05 social sciences, Bounded martingale, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Doob's martingale inequality, Diffusion process, Conic section, Quantitative Finance - Mathematical Finance, Azuma's inequality, Local martingale, symbols, Martingale difference sequence, stochastic survival probability, diffusion process, Martingale (probability theory), Mathematics - Probability, Social Sciences (miscellaneous), Finance
Abstract: In this paper we introduce the concept of conic martingales}. This class refers to stochastic processes having the martingale property, but that evolve within given (possibly time-dependent) boundaries. We first review some results about the martingale property of solution to driftless stochastic differential equations. We then provide a simple way to construct and handle such processes. Specific attention is paid to martingales in $[0,1]$. One of these martingales proves to be analytically tractable. It is shown that up to shifting and rescaling constants, it is the only martingale (with the trivial constant, Brownian motion and Geometric Brownian motion) having a separable coefficient $\sigma(t,y)=g(t)h(y)$ and that can be obtained via a time-homogeneous mapping of Gaussian diffusions. The approach is exemplified to the modeling of stochastic conditional survival probabilities in the univariate (both conditional and unconditional to survival) and bivariate cases., Comment: 34 pages, 5 figures
Published: 2017
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4. Variational Inference for Stochastic Block Models From Sampled Data

Author: Pierre Barbillon, Julien Chiquet, Timothée Tabouy, Mathématiques et Informatique Appliquées (MIA-Paris), AgroParisTech-Institut National de la Recherche Agronomique (INRA), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), INRA MetaProgram 'GloFoods' through the project 'SEARS' French National research Agency (ANR): 'Investissement d'Avenir' program, through the 'IDI 2017' project - IDEX Paris-Saclay ANR-11-IDEX-0003-02 French National research Agency (ANR): 'EcoNet' project, and Institut National de la Recherche Agronomique (INRA)-AgroParisTech
Subjects: Statistics and Probability, FOS: Computer and information sciences, 0303 health sciences, Mathematical optimization, Computer science, Missing data, Stochastic block model, Inference, Sampling (statistics), Sampled network, 01 natural sciences, Methodology (stat.ME), 010104 statistics & probability, 03 medical and health sciences, Block (telecommunications), 0101 mathematics, Statistics, Probability and Uncertainty, Variational inference, [STAT.ME]Statistics [stat]/Methodology [stat.ME], Statistics - Methodology, 030304 developmental biology
Abstract: International audience; This article deals with nonobserved dyads during the sampling of a network and consecutive issues in the inference of the stochastic block model (SBM). We review sampling designs and recover missing at random (MAR) and not missing at random (NMAR) conditions for the SBM. We introduce variants of the variational EM algorithm for inferring the SBM under various sampling designs (MAR and NMAR) all available as an R package. Model selection criteria based on integrated classification likelihood are derived for selecting both the number of blocks and the sampling design. We investigate the accuracy and the range of applicability of these algorithms with simulations. We explore two real-world networks from ethnology (seed circulation network) and biology (protein–protein interaction network), where the interpretations considerably depend on the sampling designs considered. Supplementary materials for this article are available online.
Published: 2019
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5. Lamn property for the drift and volatility parameters of a SDE driven by a stable LEVY process

Author: Emmanuelle Clément, Huong Nguyen, Arnaud Gloter, Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec, Fédération de Mathématiques de l'Ecole Centrale Paris (FR3487), Ecole Centrale Paris-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Centre National de la Recherche Scientifique (CNRS)-Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE, Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Clément, Emmanuelle, Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Ecole Centrale Paris, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Analyse, Géométrie et Modélisation (AGM - UMR 8088), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), Laboratoire de Physique des Solides (LPS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire d'Ingénierie des Systèmes Biologiques et des Procédés (LISBP), Institut National de la Recherche Agronomique (INRA)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), and Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, Mathematical optimization, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], media_common.quotation_subject, 01 natural sciences, Lévy process, Stable process, 010104 statistics & probability, symbols.namesake, Stochastic differential equation, 0101 mathematics, [MATH]Mathematics [math], Fisher information, Normality, media_common, Mathematics, 010102 general mathematics, Mathematical analysis, [STAT] Statistics [stat], Parametric estimation, MSC2010: primary 60G51, 62F12, 60H07, secondary 60F05, 60G52, 60J75, [STAT]Statistics [stat], [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], LAMN property, symbols, Jump, Volatility (finance), Drift coefficient, Malliavin calculus for jump processes
Abstract: This work focuses on the local asymptotic mixed normality (LAMN) property from high frequency observations, of a continuous time process solution of a stochastic differential equation driven by a truncated α-stable process with index α ∈ (0, 2). The process is observed on the fixed time interval [0,1] and the parameters appear in both the drift coefficient and scale coefficient. This extends the results of Clément and Gloter [Stoch. Process. Appl. 125 (2015) 2316–2352] where the index α ∈ (1, 2) and the parameter appears only in the drift coefficient. We compute the asymptotic Fisher information and find that the rate in the LAMN property depends on the behavior of the Lévy measure near zero. The proof relies on the small time asymptotic behavior of the transition density of the process obtained in Clément et al. [Preprint HAL-01410989v2 (2017)].
Published: 2019
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6. C-mix: a high dimensional mixture model for censored durations, with applications to genetic data

Author: Bussy, Simon, Guilloux, Agathe, Gaïffas, Stéphane, Jannot, Anne-Sophie, Laboratoire de Statistique Théorique et Appliquée (LSTA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Hôpital Européen Georges Pompidou [APHP] (HEGP), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpitaux Universitaires Paris Ouest - Hôpitaux Universitaires Île de France Ouest (HUPO), Centre de Recherche des Cordeliers (CRC), Université Pierre et Marie Curie - Paris 6 (UPMC)-École pratique des hautes études (EPHE), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM), Bussy, Simon, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Université Pierre et Marie Curie - Paris 6 (UPMC)-École Pratique des Hautes Études (EPHE), Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Université Pierre et Marie Curie - Paris 6 (UPMC), Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Assistance publique - Hôpitaux de Paris (AP-HP) (APHP)-Hôpitaux Universitaires Paris Ouest - Hôpitaux Universitaires Île de France Ouest (HUPO), and Université Paris Diderot - Paris 7 (UPD7)-École pratique des hautes études (EPHE)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM)
Subjects: FOS: Computer and information sciences, Mixture duration model, High-dimensional estimation, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Machine Learning (stat.ML), Elastic-net reg- ularization, Survival analysis, Coxs proportional hazards model, CURE model, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML]
Abstract: International audience; We introduce a supervised learning mixture model for censored durations (C-mix) to simultaneously detect subgroups of patients with different prognosis and order them based on their risk. Our method is applicable in a high-dimensional setting, i.e. with a large number of biomedical covariates. Indeed, we penalize the negative log-likelihood by the Elastic-Net, which leads to a sparse parameterization of the model and automatically pinpoints the relevant covariates for the survival prediction. Inference is achieved using an efficient Quasi-Newton Expectation Maximization (QNEM) algorithm, for which we provide convergence properties. The statistical performance of the method is examined on an extensive Monte Carlo simulation study, and finally illustrated on three publicly available genetic cancer datasets with high-dimensional co-variates. We show that our approach outperforms the state-of-the-art survival models in this context, namely both the CURE and Cox proportional hazards models penalized by the Elastic-Net, in terms of C-index, AUC(t) and survival prediction. Thus, we propose a powerfull tool for personalized medicine in cancerology.
Published: 2019

7. Indifference fee rate for variable annuities

Author: Etienne Chevalier, Ricardo Romo Romero, Thomas Lim, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), and Chevalier, Etienne
Subjects: Stochastic control, 050208 finance, Actuarial science, [QFIN.PM]Quantitative Finance [q-fin]/Portfolio Management [q-fin.PM], Applied Mathematics, Variable annuities, 05 social sciences, Utility maximization, backward stochastic differential equation, utility maximization, [QFIN.PM] Quantitative Finance [q-fin]/Portfolio Management [q-fin.PM], 01 natural sciences, indifference pricing, Variable annuities,indifference pricing,stochastic control,utility maximization,backward stochastic differential equation, 010104 statistics & probability, Stochastic differential equation, 0502 economics and business, Arbitrage pricing theory, Economics, stochastic control, 0101 mathematics, Mathematical economics, Finance, Indifference curve, Valuation (finance)
Abstract: In this paper, we work on indifference valuation of variable annuities and give a computation method for indifference fees. We focus on the guaranteed minimum death benefits (GMDB) and the guaranteed minimum living benefits (GMLB) and allow the policyholder to make withdrawals. We assume that the fees are continuously paid and that the fee rate is fixed at the beginning of the contract. Following indifference pricing theory, we define indifference fee rate for the insurer as a solution of an equation involving two stochastic control problems. Relating these problems to backward stochastic differential equations (BSDEs) with jumps, we provide a verification theorem and give the optimal strategies associated to our control problems. From these, we derive a computation method to get indifference fee rates. We conclude our work with numerical illustrations of indifference fees sensibilities with respect to parameters.
Published: 2016
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8. Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates

Author: Agathe Guilloux, Marie-Luce Taupin, Sarah Lemler, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Statistique Théorique et Appliquée (LSTA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec, Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de la Recherche Agronomique (INRA), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), INRA - Mathématiques et Informatique Appliquées (Unité MIAJ), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie - Paris 6 (UPMC), Laboratoire de Mathématiques et Modélisation d'Evry, Polytechnique - X - Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS) - Université Pierre et Marie Curie - Paris 6 (UPMC), Laboratoire de mathématiques et informatique pour la complexité et les systèmes (Châtenay-Malabry, Hauts de Seine), and Unité MaIAGE
Subjects: FOS: Computer and information sciences, Statistics and Probability, Statistics::Theory, Kernel density estimation, [MATH] Mathematics [math], 010103 numerical & computational mathematics, Semi-parametric model, Statistics - Applications, Counting process, 01 natural sciences, Non-asymptotic oracle inequality, Methodology (stat.ME), 010104 statistics & probability, Minimum-variance unbiased estimator, [STAT.AP] Statistics [stat]/Applications [stat.AP], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistics, Consistent estimator, Applications (stat.AP), [MATH]Mathematics [math], 0101 mathematics, Statistics - Methodology, ComputingMilieux_MISCELLANEOUS, Goldenshluger and Lepski method, Mathematics, [STAT.AP]Statistics [stat]/Applications [stat.AP], Numerical Analysis, [STAT.ME] Statistics [stat]/Methodology [stat.ME], [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Estimator, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Survival analysis, Kernel estimation, Efficient estimator, Variable kernel density estimation, Statistics, Probability and Uncertainty, Minimax estimator, [STAT.ME]Statistics [stat]/Methodology [stat.ME], Invariant estimator, Conditional hazard rate function
Abstract: The aim of this article is to propose a novel kernel estimator of the baseline function in a general high-dimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the regression parameter in the Cox model via a Lasso procedure. We then plug this estimator into the classical kernel estimator of the baseline function, obtained by smoothing the so-called Breslow estimator of the cumulative baseline function. We propose and study an adaptive procedure for selecting the bandwidth, in the spirit of Gold-enshluger and Lepski (2011). We state non-asymptotic oracle inequalities for the final estimator, which reveal the reduction of the rates of convergence when the dimension of the covariates grows.
Published: 2016
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9. A general HJM framework for multiple yield curve modelling

Author: Alessandro Gnoatto, Christa Cuchiero, Claudio Fontana, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Fontana, Claudio, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), and Benassù, Serena
Subjects: Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [QFIN.PR]Quantitative Finance [q-fin]/Pricing of Securities [q-fin.PR], affine processes, semimartingale, [QFIN.PR] Quantitative Finance [q-fin]/Pricing of Securities [q-fin.PR], forward rate agreement, 01 natural sciences, FOS: Economics and business, 010104 statistics & probability, Basis swap, 0502 economics and business, Economics, Econometrics, FOS: Mathematics, Applied mathematics, Multiple yield curves, HJM model, Semimartingale, Forward rate agreement, Libor rate, Affine processes, Multiplicative spreads, 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Mathematics, Valuation (algebra), 050208 finance, Heath–Jarrow–Morton framework, Libor rate, Interest rate derivative, Mathematical finance, 05 social sciences, Multiplicative function, Probability (math.PR), Multiplicative spreads, Multiple yield curves, 91G30, 91B24, 91B70, Mathematical Finance (q-fin.MF), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Semimartingale, Affine processes, Forward rate agreement, HJM model, Finance, Quantitative Finance - Mathematical Finance, Forward rate, JEL: E - Macroeconomics and Monetary Economics/E.E4 - Money and Interest Rates/E.E4.E43 - Interest Rates: Determination, Term Structure, and Effects, Affine transformation, Yield curve, Statistics, Probability and Uncertainty, Mathematics - Probability, interest rate, JEL: G - Financial Economics/G.G1 - General Financial Markets/G.G1.G12 - Asset Pricing • Trading Volume • Bond Interest Rates
Abstract: We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is specified as an affine process, we obtain a flexible Markovian structure. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling., Comment: (40 pages, 4 figures)
Published: 2016

10. Matching for the nonconventional MHC-I MICA gene significantly reduces the incidence of acute and chronic GVHD

Author: Christophe Picard, Cécile Macquin, Sergi Querol, Catherine Paillard, Katharina Fleischhauer, Gaëlle Giacometti, Bronno van der Holt, Ibrahim Yakoub-Agha, Wassila Ilias, Anne Cesbron, Myriam Labopin, Masao Ota, Jorge Sierra, Fabio Ciceri, Dominique Charron, Ryad Tamouza, Régis Peffault de Latour, Xavier Lafarge, Katia Gagne, Seiamak Bahram, Myriam Maumy-Bertrand, Meiggie Untrau, Pascale Loiseau, Raphael Carapito, Jürgen Kuball, Bruno Lioure, Frans H.J. Claas, Noel Milpied, Antoine Toubert, Jan J. Cornelissen, Irina Kotova, Philippe Moreau, Eric Spierings, Mauricette Michallet, Arnon Nagler, Annette Schmitt-Graeff, Angélique Pichot, Petya Apostolova, Mohamad Mohty, Aurore Morlon, Myriam Labalette, Nicolas Jung, Didier Blaise, Yoshihiko Katsuyama, Hidetoshi Inoko, A. Parissiadis, Frédéric Bertrand, Marius Kwemou, Sandra Michel, Machteld Oudshoorn, Gérard Socié, Robert Zeiser, Peter A. von dem Borne, Valérie Dubois, Luca Vago, Carapito, Raphael, Jung, Nicola, Kwemou, Mariu, Untrau, Meiggie, Michel, Sandra, Pichot, Angélique, Giacometti, Gaëlle, Macquin, Cécile, Ilias, Wassila, Morlon, Aurore, Kotova, Irina, Apostolova, Petya, Schmitt Graeff, Annette, Cesbron, Anne, Gagne, Katia, Oudshoorn, Machteld, Van Der Holt, Bronno, Labalette, Myriam, Spierings, Eric, Picard, Christophe, Loiseau, Pascale, Tamouza, Ryad, Toubert, Antoine, Parissiadis, Anne, Dubois, Valérie, Lafarge, Xavier, Maumy Bertrand, Myriam, Bertrand, Frédéric, Vago, Luca, Ciceri, Fabio, Paillard, Catherine, Querol, Sergi, Sierra, Jorge, Fleischhauer, Katharina, Nagler, Arnon, Labopin, Myriam, Inoko, Hidetoshi, Von Dem Borne, Peter A., Kuball, Jürgen, Ota, Masao, Katsuyama, Yoshihiko, Michallet, Mauricette, Lioure, Bruno, De Latour, Régis Peffault, Blaise, Didier, Cornelissen, Jan J., Yakoub Agha, Ibrahim, Claas, Fran, Moreau, Philippe, Milpied, Noël, Charron, Dominique, Mohty, Mohamad, Zeiser, Robert, Socié, Gérard, Bahram, Seiamak, inconnu, Inconnu, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Immuno-Rhumatologie Moléculaire, Université de Strasbourg (UNISTRA)-Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), laboratoire d'Etudes et de recherches en Statistiques et Développement (LERSTAD), Université Gaston Bergé Sénégal, Laboratoire d'Acoustique Environnementale (IFSTTAR/AME/LAE), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université de Lyon-PRES Université Nantes Angers Le Mans (UNAM), Physique des interactions ioniques et moléculaires (PIIM), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS), LabEx Transplantex [Strasbourg], Université de Strasbourg (UNISTRA), Etablissement Français du Sang [Nantes], Etablissement Français du Sang - Alpes-Méditerranée (EFS - Alpes-Méditerranée), Etablissement Français du Sang, Service de pneumologie [Rennes] = Pneumology [Rennes], CHU Pontchaillou [Rennes], Anthropologie bio-culturelle, Droit, Ethique et Santé (ADES), Aix Marseille Université (AMU)-EFS ALPES MEDITERRANEE-Centre National de la Recherche Scientifique (CNRS), Alloimmunité-Autoimmunité-Transplantation (A2T), Institut Universitaire d'Hématologie (IUH), Université Paris Diderot - Paris 7 (UPD7)-Université Paris Diderot - Paris 7 (UPD7)-Institut National de la Santé et de la Recherche Médicale (INSERM), Hématologie -Immunologie -Cibles thérapeutiques, Université Paris Diderot - Paris 7 (UPD7)-Institut National de la Santé et de la Recherche Médicale (INSERM), Hôpital Saint-Louis, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université Paris Diderot - Paris 7 (UPD7), Sociétés, Acteurs, Gouvernement en Europe (SAGE), Politique, Religion, Institutions et Sociétés : Mutations Européennes - Groupe de Sociologie Politique Européenne (PRISME-GSPE), Centre National de la Recherche Scientifique (CNRS), Centre de Transfusion Sanguine Aquitaine-Limousin (CTS AQUITAINE-LIMOUSIN), Centre de Transfusion Sanguine, Ospedale San Raffaele, Université Pierre et Marie Curie - Paris 6 - UFR de Médecine Pierre et Marie Curie (UPMC), Université Pierre et Marie Curie - Paris 6 (UPMC), Barcelona Cord Blood Bank, Agrosystèmes tropicaux (ASTRO), Institut National de la Recherche Agronomique (INRA), Chaim Sheba Medical Center [Ramat Gan, Israel], CHU Saint-Antoine [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU), Hôpital Edouard Herriot [CHU - HCL], Hospices Civils de Lyon (HCL), Département d'Oncologie et Hématologie [Strasbourg], Les Hôpitaux Universitaires de Strasbourg (HUS), Université Paris Diderot - Paris 7 (UPD7), Erasmus University Medical Center [Rotterdam] (Erasmus MC), Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Department of Immunohematology and Blood Transfusion, Leiden University Medical Center (LUMC), Universiteit Leiden-Universiteit Leiden, Centre hospitalier universitaire de Nantes (CHU Nantes), Centre d'Investigations Biomédicales-Hématologie, Oncologie et Greffes (CIB-HOG), Hôpital St Louis, Assistance Publique des Hôpitaux de Paris (AP-HP), Centre d'Investigations Biomédicales-Hématologie, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Service de pneumologie, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-CHU Pontchaillou [Rennes], Assistance publique - Hôpitaux de Paris (AP-HP) (APHP)-Université Paris Diderot - Paris 7 (UPD7), Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), ALWP-EBMT & Département d'hématologie et de thérapie cellulaire [AP-HP Hôpital Saint-Antoine], AP-HP - Hôpital Saint-Antoine, Hematology, Institut de Recherche Mathématique Avancée ( IRMA ), Université de Strasbourg ( UNISTRA ) -Centre National de la Recherche Scientifique ( CNRS ), Université de Strasbourg ( UNISTRA ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ), Laboratoire de Mathématiques et Modélisation d'Evry ( LaMME ), Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -ENSIIE-Centre National de la Recherche Scientifique ( CNRS ), laboratoire d'Etudes et de recherches en Statistiques et Développement ( LERSTAD ), Laboratoire d'Acoustique Environnementale ( IFSTTAR/AME/LAE ), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux ( IFSTTAR ) -Université de Lyon-PRES Université Nantes Angers Le Mans ( UNAM ), Laboratoire d'Histoire des Sciences et de Philosophie - Archives Henri Poincaré ( LHSP ), Université de Lorraine ( UL ) -Centre National de la Recherche Scientifique ( CNRS ), Physique des interactions ioniques et moléculaires ( PIIM ), Aix Marseille Université ( AMU ) -Centre National de la Recherche Scientifique ( CNRS ), Functional Genomics and Cancer, Etablissement Français du Sang - Alpes-Méditerranée ( EFS - Alpes-Méditerranée ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -CHU Pontchaillou [Rennes], Anthropologie bio-culturelle, Droit, Ethique et Santé ( ADES ), Aix Marseille Université ( AMU ) -EFS ALPES MEDITERRANEE-Centre National de la Recherche Scientifique ( CNRS ), Alloimmunité-Autoimmunité-Transplantation ( A2T ), Université Paris Diderot - Paris 7 ( UPD7 ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ), Assistance publique - Hôpitaux de Paris (AP-HP)-Université Paris Diderot - Paris 7 ( UPD7 ), Sociétés, Acteurs, Gouvernement en Europe ( SAGE ), Politique, Religion, Institutions et Sociétés : Mutations Européennes - Groupe de Sociologie Politique Européenne ( PRISME-GSPE ), Centre National de la Recherche Scientifique ( CNRS ), Centre de Transfusion Sanguine Aquitaine-Limousin ( CTS AQUITAINE-LIMOUSIN ), Géographie de l'environnement ( GEODE ), Centre National de la Recherche Scientifique ( CNRS ) -Université Toulouse - Jean Jaurès ( UT2J ), Université Pierre et Marie Curie - Paris 6 - UFR de Médecine Pierre et Marie Curie ( UPMC ), Université Pierre et Marie Curie - Paris 6 ( UPMC ), Agrosystèmes tropicaux ( ASTRO ), Institut National de la Recherche Agronomique ( INRA ), Hospices Civils de Lyon ( HCL ), IFR Saint-Louis, institut d'hématologie ( ISLIH ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Assistance publique - Hôpitaux de Paris (AP-HP)-Université Paris Diderot - Paris 7 ( UPD7 ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Centre National de la Recherche Scientifique ( CNRS ), Erasmus MC University medical Centre / Daniel den Hoed Cancer centre, Centre Hospitalier Régional Universitaire [Lille] ( CHRU Lille ), Centre hospitalier universitaire de Nantes ( CHU Nantes ), Laboratoire de Mathématiques et Modélisation d'Evry, PRES Université Nantes Angers Le Mans (UNAM)-Université de Lyon-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université, Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Strasbourg (UNISTRA), Centre National de la Recherche Scientifique (CNRS)-ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA), Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut Universitaire d'Hématologie (IUH), Université Paris Diderot - Paris 7 (UPD7)-Université Paris Diderot - Paris 7 (UPD7), Université Paris Diderot - Paris 7 (UPD7)-Assistance publique - Hôpitaux de Paris (AP-HP) (APHP), and Université Paris Diderot - Paris 7 (UPD7)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)
Subjects: 0301 basic medicine, Male, medicine.medical_treatment, [SDV]Life Sciences [q-bio], Medizin, Graft vs Host Disease, Hematopoietic stem cell transplantation, Biochemistry, Linkage Disequilibrium, immune system diseases, HLA Antigens, Cytotoxic T cell, Child, ComputingMilieux_MISCELLANEOUS, HLA-DQB1, biology, Histocompatibility Testing, Incidence, Hematopoietic Stem Cell Transplantation, Hematology, Middle Aged, Allografts, 3. Good health, surgical procedures, operative, NK Cell Lectin-Like Receptor Subfamily K, Child, Preschool, Acute Disease, [SDV.IMM]Life Sciences [q-bio]/Immunology, Female, Adult, Adolescent, Immunology, Human leukocyte antigen, 03 medical and health sciences, MHC class I, medicine, Journal Article, Humans, Aged, Retrospective Studies, Transplantation, [ SDV ] Life Sciences [q-bio], Histocompatibility Antigens Class I, Infant, Newborn, Infant, Cell Biology, medicine.disease, Histocompatibility, stomatognathic diseases, 030104 developmental biology, Graft-versus-host disease, Chronic Disease, biology.protein
Abstract: Graft-versus-host disease (GVHD) is among the most challenging complications in unrelated donor hematopoietic cell transplantation (HCT). The highly polymorphic MHC class I chain-related gene A, MICA, encodes a stress-induced glycoprotein expressed primarily on epithelia. MICA interacts with the invariant activating receptor NKG2D, expressed by cytotoxic lymphocytes, and is located in the MHC, next to HLA-B. Hence, MICA has the requisite attributes of a bona fide transplantation antigen. Using high-resolution sequence-based genotyping of MICA, we retrospectively analyzed the clinical effect of MICA mismatches in a multicenter cohort of 922 unrelated donor HLA-A, HLA-B, HLA-C, HLA-DRB1, and HLA-DQB1 10/10 allele-matched HCT pairs. Among the 922 pairs, 113 (12.3%) were mismatched in MICA. MICA mismatches were significantly associated with an increased incidence of grade III-IV acute GVHD (hazard ratio [HR], 1.83; 95% confidence interval [CI], 1.50-2.23; P < .001), chronic GVHD (HR, 1.50; 95% CI, 1.45-1.55; P < .001), and nonelapse mortality (HR, 1.35; 95% CI, 1.24-1.46; P < .001). The increased risk for GVHD was mirrored by a lower risk for relapse (HR, 0.50; 95% CI, 0.43-0.59; P < .001), indicating a possible graft-versus-leukemia effect. In conclusion, when possible, selecting a MICA-matched donor significantly influences key clinical outcomes of HCT in which a marked reduction of GVHD is paramount. The tight linkage disequilibrium between MICA and HLA-B renders identifying a MICA-matched donor readily feasible in clinical practice.
Published: 2016
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11. Espacios de Lebesgue y de Lorentz

Author: Chamorro, Diego, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry ( LaMME ), Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -ENSIIE-Centre National de la Recherche Scientifique ( CNRS ), and Chamorro, Diego
Subjects: [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], [ MATH.MATH-FA ] Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
Abstract: International audience; We study in this chapter the main properties of Lorentz spaces L p,q (X) with 0 < p ≤ +∞ and 0 < q ≤ +∞. We start with a study of Marcinkiewicz spaces L p,∞ using the distribution function d f and then we present general Lorentz spaces L p,q by using the decreasing rearrangement function f * and the maximal function f * *. Normability, Convolution, Duality of these functional spaces are the main core of this chapter.
Published: 2018

12. Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces

Author: Oscar Jarrín, Pierre Gilles Lemarié-Rieusset, Diego Chamorro, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry ( LaMME ), and Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -ENSIIE-Centre National de la Recherche Scientifique ( CNRS )
Subjects: Pure mathematics, Open problem, Mathematics::Analysis of PDEs, Type (model theory), Space (mathematics), Lebesgue integration, 01 natural sciences, Physics::Fluid Dynamics, symbols.namesake, Navier–Stokes equations, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Analysis of PDEs, Trivial solution, stationary system, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, 0101 mathematics, Mathematical Physics, Mathematics, Applied Mathematics, 010102 general mathematics, Morrey spaces, 010101 applied mathematics, symbols, Liouville theorem, Analysis, Analysis of PDEs (math.AP)
Abstract: Uniqueness of Leray solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations in the whole space R 3 . Under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution U → = 0 is the unique solution. This type of results are known as Liouville theorems.
Published: 2018

13. Frequency decay for Navier-Stokes stationary solutions

Author: Chamorro, Diego, Jarrin, Oscar, Lemarié-Rieusset, Pierre Gilles, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Physics::Fluid Dynamics, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Analysis of PDEs (math.AP)
Abstract: We consider stationary Navier-Stokes equations in R 3 with a regular external force and we prove exponential frequency decay of the solutions. Moreover, if the external force is small enough, we give a pointwise exponential frequency decay for such solutions according to the K41 theory. If a damping term is added to the equation, a pointwise decay is obtained without the smallness condition over the force.
Published: 2017

14. Sobolev multipliers, maximal functions and parabolic equations with a quadratic nonlinearity

Author: Pierre Gilles Lemarié-Rieusset, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Lemarié-Rieusset, Pierre Gilles, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry
Subjects: Class (set theory), maximal function, 2010 Mathematics Subject Classification : 35K57, 35B35, Mathematics::Analysis of PDEs, 35B35, 01 natural sciences, Physics::Fluid Dynamics, Navier–Stokes equations, Hedberg inequality, multipliers, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics, Cauchy problem, 010102 general mathematics, Mathematical analysis, Quadratic nonlinearity, Morrey spaces, semilinear parabolic equations, Parabolic partial differential equation, 010101 applied mathematics, Sobolev space, Besov spaces, Dissipative system, Maximal function, Keller–Segel equations, Triebel, Analysis
Abstract: We develop a general framework to describe global mild solutions to a Cauchy problem with small initial values concerning a general class of semilinear parabolic equations with a quadratic nonlinearity. This class includes the Navier–Stokes equations, the subcritical dissipative quasi-geostrophic equation and the parabolic–elliptic Keller–Segel system.
Published: 2017

15. Controlling the occupation time of an exponential martingale

Author: Monique Jeanblanc, Christophette Blanchet-Scalliet, Stefan Ankirchner, Institut für Mathematik, Friedrich-Schiller-Universität = Friedrich Schiller University Jena [Jena, Germany], Probabilités, statistique, physique mathématique (PSPM), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université d'Évry-Val-d'Essonne (UEVE), Friedrich-Schiller-Universität Jena, Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Friedrich Schiller Universität [Jena, Germany], École Centrale de Lyon (ECL) - Université Claude Bernard Lyon 1 (UCBL) - Université Jean Monnet - Saint-Etienne - Institut National des Sciences Appliquées (INSA) - Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Université d'Evry-Val d'Essonne, Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Discrete mathematics, Geometric Brownian motion, Control and Optimization, Applied Mathematics, 010102 general mathematics, Sigma, Rigorous proof, [MATH] Mathematics [math], Optimal control, 01 natural sciences, Exponential function, 010104 statistics & probability, Calculus, Local martingale, 0101 mathematics, Volatility (finance), [MATH]Mathematics [math], Martingale (probability theory), Mathematics
Abstract: We consider the problem of maximizing the expected amount of time an exponential martingale spends above a constant threshold up to a finite time horizon. We assume that at any time the volatility of the martingale can be chosen to take any value between $\sigma _1$ and $\sigma _2$, where $0 < \sigma _1 < \sigma _2$. The optimal control consists in choosing the minimal volatility $\sigma _1$ when the process is above the threshold, and the maximal volatility if it is below. We give a rigorous proof using classical verification and provide integral formulas for the maximal expected occupation time above the threshold.
Published: 2017
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16. An enlargement of filtration formula with applications to multiple non-ordered default times

Author: Shiqi Song, Libo Li, Monique Jeanblanc, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), University of New South Wales [Sydney] (UNSW), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), JEANBLANC, Monique, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Enlargement of filtration, Financial economics, Type (model theory), 01 natural sciences, JEL classification G14 Mathematics Subject Classification (2010) 60G07 · 91G40, Combinatorics, 010104 statistics & probability, Mathematics::Probability, 0502 economics and business, Filtration (mathematics), Reduced, Semimartingale decomposition, 0101 mathematics, Mathematics, Sequence, form credit risk modeling, 050208 finance, Mathematical finance, 05 social sciences, Absolute continuity, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Semimartingale, Non-ordered default times, Statistics, Probability and Uncertainty, Finance
Abstract: In this work, for a reference filtration $\mathbb {F}$ , we develop a method for computing the semimartingale decomposition of $\mathbb {F}$ -martingales in a specific type of enlargement of $\mathbb {F}$ . As an application, we study the progressive enlargement of $\mathbb {F}$ with a sequence of non-ordered default times and show how to deduce results concerning the first-to-default, $k$ th-to-default, k-out-of-n-to-default or all-to-default events. In particular, using this method, we compute explicitly the semimartingale decomposition of $\mathbb {F}$ -martingales under the absolute continuity condition of Jacod.
Published: 2017

17. Chambres de compensation : analyse XVA, mesures de risque et applications

Author: Armenti, Yannick, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université Paris Saclay, Université d'Evry Val d'Essonne, Crépey, Stéphane, Armenti, Yannick, Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)
Subjects: JEL: C - Mathematical and Quantitative Methods, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [QFIN.CP] Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], Collatéral, Chambres de compensation (CCP), Risk Measures, [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], Counterparty Credit Risk, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Central Clearing Houses (CCP), XVA Analysis, Risque de crédit et de contrepartie, Analyse XVA, Mesures de Risque
Abstract: This thesis deals with various issues related to collateral management in the context of centralized trading through central clearing houses. In the first place, we present the notions of cost of capital and funding cost for a bank, placing them in an elementary Black–Scholes framework where the payoff of a standard call is used as the exposure at default of a counterparty. It is assumed that the bank can’t perfectly hedge this call and must face with a funding cost higher than the risk free rate, hence pricing corrections of the FVA and KVA type appear in top of the Black–Scholes price. Then, we look at the different costs that a bank has to face when trading in the CCP context. To this end, we transpose the well-known XVA analysis framework from the bilateral trading world to the central clearing one. The total cost for a member trading through a CCP is thus decomposed into aCVA corresponding to the cost for the member to reimburse its contribution to the guarantee fund in the event of losses due to the defaults of other members, a MVA which is the cost of financing its initial margin and a KVA corresponding to the cost of capital put at risk by the member in the form of its contribution to the guarantee fund. Afterwards, we question the previously used regulatory assumptions, focusing on alternatives in which members would borrow their initial margin to a third party who would post the margin instead of the member himself, and this, in exchange for remuneration. We also consider a method of computing the guarantee fund and its allocation taking into account the risk of the CCP in the sense of fluctuations of its P&L over the following year, as it results from the market risk and the counterparty risk of the members. Finally, we propose the application of multivariate risk measure methodologies for the computation of margins and/or the CCP guarantee fund. We introduce a notionof systemic risk measures in the sense that they are sensitive not only to the marginal risks of the components of a financial system (for example, but not necessarily the positions of the members of a CCP) but also to the dependence of their components., Cette thèse traite de diverses problématiques ayant trait à la gestion du collatéral dans le contexte du trading centralisé au travers des chambres de compensation. Préliminairement, nous présentons les notions de coûts de capital et coût de financement pour une banque, en les replaçant dans un cadre Black–Scholes élémentaire où le payoff d’un call standard tient lieu d’exposition au défaut d’une contrepartie. On suppose que la banque ne couvre qu’imparfaitement ce call et doit faire face à un coût de financement supérieur au taux sans risque, d’où des corrections de pricing de type FVA et KVA par rapport au prix Black–Scholes. Nous nous intéressons ensuite aux coûts auxquels une banque doit faire face lorsqu' elle trade dans le cadre d’une CCP. A cette fin, nous transposons au trading centralisé le cadre d’analyse XVA du trading bilatéral. Le coût total pour un membre de trader au travers d’une CCP est ainsi décomposé en une CVA correspondant au coût pour le membre de renflouer sa contributionau fonds de garantie en cas de pertes consécutives aux défauts d’autres membres, une MVA correspondant au coût de financement de sa marge initiale et une KVA correspondant au coût du capital mis à risque par le membre sous la forme de sa contribution au fonds de garantie. Nous remettons ensuite en cause les hypothèses réglementaires précédemment utilisées, nous intéressant à des alternatives dans lesquelles les membres auraient recours pour leur marge initiale à une tierce partie, qui posterait la marge à la place du membre en échange d’une rémunération.Nous considérons également un mode de calcul du fonds de garantie et de son allocation qui prennent en compte le risque de la chambre au sens des fluctuations de son P&L sur l’année suivante, tel qu’il résulte de la combinaison des risque de marché et des risques de défaut des membres. Enfin, nous proposons l’application de méthodologies de type mesures de risque multivariées pour le calcul des marges et/ou du fonds de garantie des membres. Nous introduisons une notion de mesures de risque systémiques au sens où elles présentent une sensibilité non seulementaux risques marginaux des composantes d’un système financier (par exemple, mais non nécessairement, les positions des membres d’une CCP), mais aussi à leur dépendance.
Published: 2017

18. Difficulty influence on motivation over time in video games using survival analysis

Author: Thibault Allart, Agathe Guilloux, Stéphane Natkin, Michel Pierfitte, Guillaume Levieux, CEDRIC - Interactivité pour Lire et Jouer (CEDRIC - ILJ), Centre d'études et de recherche en informatique et communications (CEDRIC), Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE)-Conservatoire National des Arts et Métiers [CNAM] (CNAM), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE)-Conservatoire National des Arts et Métiers [CNAM] (CNAM), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), Ubisoft, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE)-Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE)-Conservatoire National des Arts et Métiers [CNAM] (CNAM), Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)
Subjects: Motivation, Multimedia, Computer science, Computer games, 020207 software engineering, 02 engineering and technology, Division (mathematics), computer.software_genre, 01 natural sciences, Game analytics, Survival Analysis, Game Analytics, 010104 statistics & probability, Video Games, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 0202 electrical engineering, electronic engineering, information engineering, [INFO]Computer Science [cs], Challenge, 0101 mathematics, Link (knot theory), Attribution, computer, Difficulty, Cognitive psychology, Avatar
Abstract: International audience; In this paper, we study the link between difficulty and player's motivation in two games developed by Ubisoft®: Rayman®Legends and Tom Clancy's the Division®. We describe a method to estimate players' difficulty over time and link it's time varying effect with players retention. Results confirm flow and self-efiicacy theory. Also, for the firrst hours of playtime, results differ between the two games. We explain that discrepancy with regard to attribution theory : in Rayman Legends, failure can be mainly attributed to the player skills, while in Tom Clancy's the Division, avatar's strength plays a fundamental role and can always be relatively quickly improved.; Cet article étudie le lien entre la difficulté et la motivation des joueurs dans deux jeux développés par Ubisoft : Rayman®Legends et Tom Clancy's the Division®. Nous décrivons une méthode d'estimation de la difficulté en fonction du temps, ainsi que son lien avec la rétention des joueurs. Ces résultats sont cohérents avec la théroie du flow et le sentiment d'auto efficacité. Egalement, pour les premières heures de jeu, les résultats diffèrent selon les jeux. Nous expliquons cette différence a l'aide de la théorie de l'attribution : dans Rayman Legends, l'échec peut être principalement attribué au niveau de maitrise du joueur, alors que pour Tom Clancy's the Division, les caractéristiques de l'avatar jouent un rôle fondamental et peuvent toujours être rapidement améliorées.
Published: 2017
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19. The local energy inequalities in the theory of the Navier-Stokes equations

Author: Mayoufi, Kawther, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université d'Evry Val d'Essonne, Pierre Gilles Lemarié-Rieusset, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Mayoufi, Kawther
Subjects: Théorie de Caffarelli, Équations de Navier-Stokes, Partial regularity of the Navier-Stokes equations, Navier-stokes equations, Stability of weak dissipatives solutions of Navier-Stokes equations, Critère de Serrin, Stabilité des solutions dissipatives, [MATH] Mathematics [math], [MATH]Mathematics [math], Kohn et Nirenberg
Abstract: In this dissertation, we are concerned with the role of the local energy inequalities in the theory of the partial regularity of the weak solutions of the Navier-Stokes equations in the direction of the Theorem of Caffarelli, Kohn and Nirenberg.We distinguish three parts. The first part of the thesis deals essentially with the announcement by the Korean mathematician Choe at Waseda in 2013 of the demonstration of a new local energy inequality which applies to any weak solution of the Navier-Stokes equations without any hypothesis on the pressure, and which allowed to extend the results of partial regularity of Caffarelli, Kohn and Nirenberg to all weak solutions and not only to the suitable one.A rigorous study of the proof of Choe's inequality allowed us to conclude that this proof was false a priori for the case of a general solution, and Choe's main theorem (which was supposed to give us a regularity in time and space variables outside of an extremely small set of singularity) was contradicted by a counter-example of Serrin that linked the regularity in time to the assumptions on the pressure.In this first part, we have drafted a conscientious proof of the inequality introduced by Choe by adding an extra hypotheses that had to be introduced in order to demonstrate it. However, the new energy inequality (which did not involve the pressure) did not serve to extend Choe's assertions, but we were able to identify a new variable inspired by Choe's proof that allowed us to introduce our main result.The second part of the thesis is devoted to deeply studying the new variable suggested by a part of Choe's work. Indeed, we could assimilate a new variable $\vv$ linked to the curl of the solution $\vu$, and by studying $\vv $, using a mixture of the Serrin theory and that of Caffarelli, Kohn and Nirenberg we obtained a partial regularity result which does not apply to any weak solution (contrary to Choe's statement) but to a wider class than the suitable solutions (in the sense of Caffarelli, Kohn and Nirenberg): the notion of dissipative solutions was introduced following the work of Duchon and Robert done in 2000 and this allows us to positively include the counter example of Serrin in our new theory.The third and last part is intended for the study of the stability of dissipative solutions by weak-*convergence. Indeed, we consider a bounded sequence $\vu_{n}$ in $L^{\infty}_t L^2_x\cap L^{2}_t H^1_x$, a bounded force $\vf_{n}$ in $L^{\frac{10}{7}}_t L^{\frac{10}{7}}_x$ and a pressure $p_{n}\in \mathcal{D}'(Q)$. We also suppose that $\vu_{n}$ is dissipative in the sense of the definition given in the second part and we will prove that the limit $\vu$ of a subsequence $\vu_ {n_ {k}}$ is a solution of the Navier-Stokes equations and is dissipative., Cette thèse est consacrée au rôle des inégalités d'énergie locales dans la théorie de la régularité partielle des solutions faibles des équations de Navier-Stokes dans le sens du Théorème de Caffarelli, Kohn et Nirenberg.Nous distinguons trois parties. La première partie de la thèse traite essentiellement l'annonce faite par le mathématicien coréen Choe à Waseda en $2013$ d'une nouvelle inégalité d'énergie locale qui s'applique à toute solution faible des équations de Navier-Stokes, sans aucune hypothèse sur la pression, et qui permettait d'étendre les résultats de régularité partielle de Caffarelli, Kohn et Nirenberg à toutes les solutions faibles et pas seulement aux solutions adaptées.Une étude de la preuve de l'inégalité de Choe nous permettait de conclure que cette preuve était fausse a priori pour le cas d'une solution générale, et le théorème principal de Choe (qui était sensé nous donner une régularité en temps et en espace en dehors d'un ensemble de singularité extrêmement petit) était contredit par un contre exemple de Serrin qui liait la régularité en temps à des hypothèses sur la pression.Dans cette première partie on a rédigé une preuve rigoureuse de l'inégalité introduite par Choe en rajoutant des hypothèses supplémentaires qu'il fallait introduire pour la démontrer. Néanmoins, cette nouvelle inégalité d'énergie (qui ne fait pas intervenir la pression) nous ne sert pas à prolonger les affirmations de Choe, mais on a pu identifier une nouvelle variable, inspirée de la preuve de Choe, qui nous a permit d'introduire notre résultat principal.En effet, la deuxième partie de la thèse est consacrée à étudier profondément la nouvelle variable suggérée par une partie du travail de Choe. On a pu assimiler une nouvelle variable $\vv$ liée au rotationel de la solution $\vu$ et en étudiant $\vv$, à l'aide d'un mélange de la théorie de Serrin et celle de Caffarelli, Kohn et Nirenberg on a obtenu un résultat de régularité partielle qui ne s'applique pas à toute solution faible (contrairement à l'énoncé de Choe) mais à une classe plus large que les solutions adaptées (au sens de Caffarelli, Kohn et Nirenberg): la notion de solution dissipative a été introduite en suivant les travaux de Duchon et Robert fait en 2000 et cette notion nous permet d'inclure positivement le contre exemple de Serrin dans notre nouvelle théorie.La troisième et dernière partie de cette thèse est destinée à l'étude de la stabilité des solutions dissipatives par convergence *-faible. En effet, on considère une suite $\vu_{n}$ qui converge faiblement dans $L^{\infty}_t L^2_x\cap L^{2}_t H^1_x$, une force extérieure $\vf_{n}$ qui converge faiblement dans $L^{\frac{10}{7}}_t L^{\frac{10}{7}}_x$ à divergence nulle et une pression $p_{n}\in \mathcal{D}'(Q)$. On suppose aussi que $\vu_{n}$ est dissipative au sens de la définition donnée dans la deuxième partie et on va prouver que la limite $\vu$ d'une sous suite $\vu_{n_{k}}$ est une solution des équations de Navier-Stokes et elle est dissipative.
Published: 2017

20. Piecewise Constant Martingales and Lazy Clocks

Author: Frédéric Vrins, Christophe Profeta, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université Catholique de Louvain (UCL), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université Catholique de Louvain = Catholic University of Louvain (UCL), Profeta, Christophe, UCL - SSH/IMMAQ/CORE - Center for operations research and econometrics, UCL - SSH/IMMAQ/LFIN - Louvain Finance, and Laboratoire de Mathématiques et Modélisation d'Evry
Subjects: [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Subordinator, martingales with jumps, time changes, last passage times, Conditional expectation, bounded martingales, 01 natural sciences, Tilde, lcsh:QA75.5-76.95, G17, G44, J75, 010104 statistics & probability, Mathematics::Probability, Time-change process, Last passage time, 0502 economics and business, 0101 mathematics, Mathematics, Probability measure, Discrete mathematics, jump martingale, Time Changes, 050208 finance, martingale, 05 social sciences, Last passage times, subordinator, Martingales with jumps, Bounded martingale, Time changes, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], last passage time, Martingale, Piecewise, time-change process, lcsh:Electronic computers. Computer science, lcsh:Probabilities. Mathematical statistics, lcsh:QA273-280, Martingale (probability theory), Mathematics - Probability, Jump martingale
Abstract: This paper discusses the possibility to find and construct \textit{piecewise constant martingales}, that is, martingales with piecewise constant sample paths evolving in a connected subset of $\mathbb{R}$. After a brief review of standard possible techniques, we propose a construction based on the sampling of latent martingales $\tilde{Z}$ with \textit{lazy clocks} $\theta$. These $\theta$ are time-change processes staying in arrears of the true time but that can synchronize at random times to the real clock. This specific choice makes the resulting time-changed process $Z_t=\tilde{Z}_{\theta_t}$ a martingale (called a \textit{lazy martingale}) without any assumptions on $\tilde{Z}$, and in most cases, the lazy clock $\theta$ is adapted to the filtration of the lazy martingale $Z$. This would not be the case if the stochastic clock $\theta$ could be ahead of the real clock, as typically the case using standard time-change processes. The proposed approach yields an easy way to construct analytically tractable lazy martingales evolving on (intervals of) $\mathbb{R}$., Comment: 17 pages, 8 figures
Published: 2017

21. Identification of deregulated transcription factors involved in subtypes of cancers

Author: Champion, Magali, Chiquet, Julien, Neuvial, Pierre, Elati, Mohamed, Birmelé, Etienne, Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Mathématiques et Informatique Appliquées ( MIA-Paris ), Institut National de la Recherche Agronomique ( INRA ) -AgroParisTech, Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques et Modélisation d'Evry ( LaMME ), Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -ENSIIE-Centre National de la Recherche Scientifique ( CNRS ), Institut de biologie systémique et synthétique ( ISSB ), Université d'Évry-Val-d'Essonne ( UEVE ) -Génopole-Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique Appliquées (MIA-Paris), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Centre National de la Recherche Scientifique (CNRS)-ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA), Institut de biologie systémique et synthétique (ISSB), Université d'Évry-Val-d'Essonne (UEVE)-Génopole-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Université Paris Descartes - Paris 5 (UPD5), AgroParisTech-Institut National de la Recherche Agronomique (INRA), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)
Subjects: [STAT.AP]Statistics [stat]/Applications [stat.AP], Cancer systems biology, [ STAT.AP ] Statistics [stat]/Applications [stat.AP], Deregulation, Gene regulatory networks
Abstract: We propose a methodology for the identification of transcription factors involved in the deregulation of genes in tumoral cells. This strategy is based on the inference of a reference gene regulatory network that connects transcription factors to their downstream targets using gene expression data. The behavior of genes in tumor samples is then carefully compared to this network of reference to detect deregulated target genes. A linear model is finally used to measure the ability of each transcription factor to explain those deregulations. We assess the performance of our method by numerical experiments on a breast cancer data set. We show that the information about deregulation is complementary to the expression data as the combination of the two improves the supervised classification performance of samples into cancer subtypes.
Published: 2017

22. Joint densities of hitting times for finite state Markov processes

Author: Ali Devin Sezer, Tomasz R. Bielecki, Monique Jeanblanc, Illinois Institute of Technology (IIT), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Middle East Technical University [Ankara] (METU), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and JEANBLANC, Monique
Subjects: [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], General Mathematics, Markov process, [MATH] Mathematics [math], 01 natural sciences, Combinatorics, Finite collection, symbols.namesake, Simple (abstract algebra), finite state Markov processes, generalized phase-type distributions, Partition (number theory), Finite state, State space (physics), 0101 mathematics, [MATH]Mathematics [math], simultaneous hitting times, Mathematics, Discrete mathematics, Lebesgue measure, singular parts, 010102 general mathematics, Finite state Markov processes,simultaneous hitting times,densities of singular parts,multiple first hitting times,generalized multivariate phase-type distributions,credit risk modeling, densities of, credit risk modeling, 010101 applied mathematics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], symbols, multiple first hitting times
Abstract: For a finite state Markov process $X$ and a finite collection $\{ \Gamma_k, k \in K \}$ of subsets of its state space, let $\tau_k$ be the first time the process visits the set $\Gamma_k$. In general, $X$ may enter some of the $\Gamma_k$ at the same time and therefore the vector $\bm\tau :=(\tau_k, k \in K)$ may put nonzero mass over lower dimensional regions of ${\mathbb R}_+^{|K|}$; these regions are of the form $R_s=\{{\bm t} \in {\mathbb R}_+^{|K|}: t_i = t_j, ~~i,j \in s(1) \} \cap \bigcap_{l=2}^{|s|} \{{\bm t}:t_m < t_i = t_j,~~ i,j \in s(l), m \in s(l-1) \}$ where $s$ is any ordered partition of the set $K$ and $s(j)$ denotes the $j^{th}$ subset of $K$ in the partition $s$. When $|s| < |K|$, the density of the law of $\bm\tau$ over these regions is said to be ``singular'' because it is with respect to the $|s|$-dimensional Lebesgue measure over the region $R_s.$ We derive explicit/recursive and simple to compute formulas for these singular densities and their corresponding tail probabilities over all $R_s$ as $s$ ranges over ordered partitions of $K$. We give a numerical example and indicate the relevance of our results to credit risk modeling.
Published: 2017

23. Product Markovian quantization of an R^d -valued Euler scheme of a diffusion process with applications to finance

Author: Lucio, Fiorin, Pagès, Gilles, Sagna, Abass, Department of Mathematics, University of Padova, Italy, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Padova = University of Padua (Unipd), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Probability (math.PR), FOS: Mathematics, Mathematics - Probability
Abstract: We introduce a new approach to quantize the Euler scheme of an $\mathbb{R}^d$-valued diffusion process. This method is based on a Markovian and componentwise product quantization and allows us, from a numerical point of view, to speak of {\em fast online quantization} in dimension greater than one since the product quantization of the Euler scheme of the diffusion process and its companion weights and transition probabilities may be computed quite instantaneously. We show that the resulting quantization process is a Markov chain, then, we compute the associated companion weights and transition probabilities from (semi-) closed formulas. From the analytical point of view, we show that the induced quantization errors at the $k$-th discretization step $t_k$ is a cumulative of the marginal quantization error up to time $t_k$. Numerical experiments are performed for the pricing of a Basket call option, for the pricing of a European call option in a Heston model and for the approximation of the solution of backward stochastic differential equations to show the performances of the method.
Published: 2017

24. Stability of Densities for Perturbed Diffusions and Markov Chains

Author: Stéphane Menozzi, Valentin Konakov, Anna Kozhina, Higher School of Economics, National Research University, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), The article was prepared within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program., Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), and Menozzi, Stephane
Subjects: Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Parametrix, Markov chain, Probability (math.PR), 010102 general mathematics, Perturbation (astronomy), First order, 60H10, 65C30, 01 natural sciences, health care quality, access, and evaluation, Diffusion Processes, Holder Coefficients, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, FOS: Mathematics, Euler scheme, Statistical physics, 0101 mathematics, health care economics and organizations, Mathematics - Probability, Mathematics, Primary 60H10, Secondary 65C30
Abstract: We are interested in studying the sensitivity of diffusion processes or their approximations by Markov Chains with respect to a perturbation of the coefficients., 26 pages
Published: 2017

25. Dynamics of multivariate default system in random environment

Author: El Karoui, Nicole, Jeanblanc, Monique, Jiao, Ying, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Université Pierre et Marie Curie - Paris 6 (UPMC), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Sciences Actuarielle et Financière (SAF), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)
Subjects: [QFIN]Quantitative Finance [q-fin], Probability (math.PR), prediction process,Multiple defaults,density approach,change of probability measure, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, Mathematical Finance (q-fin.MF), FOS: Economics and business, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], prediction process, Quantitative Finance - Mathematical Finance, Risk Management (q-fin.RM), FOS: Mathematics, Multiple defaults, density approach, Mathematics - Probability, change of probability measure, Quantitative Finance - Risk Management
Abstract: International audience; We consider a multivariate default system where random environmental information is available. We study the dynamics of the system in a general setting and adopt the point of view of change of probability measures. We also make a link with the density approach in the credit risk modelling. In the particular case where no environmental information is concerned, we pay a special attention to the phenomenon of system weakened by failures as in the classical reliability system.
Published: 2017

26. Polynomial preserving diffusions on compact quadric sets

Author: Larsson, Martin, Pulido, Sergio, Department of Mathematics [ETH Zurich] (D-MATH), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), 'Chair Markets in Transition' under the aegis of Louis Bachelier laboratory, a joint initiative of École Polytechnique, Université d’Évry Val d’Essonne and Fédération Bancaire Française, and the project ANR 11-LABX-0019, SNF Grant 205121_163425, ANR-11-LABX-0019,LABEX FCD,LABEX Finance & Croissance Durable(2011), European Project: 307465,EC:FP7:ERC,ERC-2012-StG_20111012,POLYTE(2012), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology in Zürich [Zürich] (ETH Zürich), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), ANR-11-LABX-0019/11-LABX-0019,LABEX FCD,LABEX Finance & Croissance Durable(2011), Laboratoire de Mathématiques et Modélisation d'Evry, Departement of Mathematics, ETH Zurich, Eidgenössische Technische Hochschule [Zürich] (ETH ), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), 'Chair Markets in Transition' under the aegis of Louis Bachelier laboratory, a joint initiative of École Polytechnique, Université d’Évry Val d’Essonne and Fédération Bancaire Française, and European Project : 307465, EC:FP7:ERC, ERC-2012-StG_20111012, POLYTE(2012)
Subjects: sums of squares, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], stochastic invariance, MSC2010 subject classifications: 60J60, 60H10, 11E25, Polynomial preserving processes, biquadratic forms, pathwise uniqueness, smooth densities, MSC2010: 60J60, 60H10, 11E25
Abstract: International audience; Polynomial preserving processes are defined by the property that conditional expectations of polynomial functions of the process are again polynomials of the same or lower degree. Many fundamental stochastic processes, including affine processes, are polynomial preserving, and their tractable structure makes them important in applications. In this paper we study polynomial preserving diffusions whose state space is a compact quadric set. Necessary and sufficient conditions for existence, uniqueness, and boundary attainment are given. The existence of a convenient parameterization of the generator is shown to be closely related to the classical problem of expressing nonnegative polynomials---specifically, biquadratic forms vanishing on the diagonal---as a sum of squares. We prove that in dimension $d\le 4$ every such biquadratic form is a sum of squares, while for $d\ge6$ there are counterexamples. The case $d=5$ remains open. An equivalent probabilistic description of the sum of squares property is provided, and we show how it can be used to obtain results on pathwise uniqueness and existence of smooth densities.
Published: 2017
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27. Fully non-homogeneous problem of two-dimensional second grade fluids

Author: Bernard, Jean Marie, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry
Subjects: Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Analysis of PDEs (math.AP)
Abstract: This article studies the solutions of a two-dimensional grade-two fluid model with a fully non-homogeneous boundary condition for velocity u. Compared to problems with a homogeneous or tangential boundary condition, studied by many authors , we must add a boundary condition, otherwise the problem is no longer well-posed. We propose two conditions on z = curl (u -- $\alpha$$\Delta$u), which differ according to the regularity of z, on the portion of $\partial$$\Omega$ where $\alpha$u. n \textless{} 0. Following the approach of V. Girault and L.R. Scott in the tangential boundary case, we split the problem into a system with a generalized Stokes problem and a transport problem. But, compared to the study of these authors, we are now led to solve transport problems with boundary conditions. In two previous articles, we studied these transport problems. The results obtained in these articles allow us, by a fixed-point argument, to establish existence of the solutions for the fully non-homogeneous grade-two problem. Uniqueness requires the boundary condition with z in H 1 .
Published: 2017

28. Invariance properties in the dynamic gaussian copula model *

Author: Shiqi Song, Stéphane Crépey, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Computational Finance (q-fin.CP), 01 natural sciences, Measure (mathematics), CDS, [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], FOS: Economics and business, 010104 statistics & probability, Quantitative Finance - Computational Finance, immersion property, 0502 economics and business, Feature (machine learning), Econometrics, QA1-939, invariance, 0101 mathematics, invariance time, time, Mathematics, Probability measure, T57-57.97, 050208 finance, Applied mathematics. Quantitative methods, dynamic copula, 05 social sciences, Maxima and minima, counterparty credit risk, Gaussian copula, wrong-way risk, Credit derivative, Counterparty, Value (mathematics), Credit risk
Abstract: We prove that the default times (or any of their minima) in the dynamic Gaussian copula model of Cr{\'e}pey, Jeanblanc, and Wu (2013) are invariance times in the sense of Cr{\'e}pey and Song (2017), with related invariance probability measures different from the pricing measure. This reflects a departure from the immersion property, whereby the default intensities of the surviving names and therefore the value of credit protection spike at default times. These properties are in line with the wrong-way risk feature of counterparty risk embedded in credit derivatives, i.e. the adverse dependence between the default risk of a counterparty and an underlying credit derivative exposure.
Published: 2017

29. INVARIANCE TIMES *

Author: Crépey, Stéphane, Song, Shiqi, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, 050208 finance, 05 social sciences, measure change, Computational Finance (q-fin.CP), 01 natural sciences, [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], FOS: Economics and business, mathematical finance, 010104 statistics & probability, Quantitative Finance - Computational Finance, Mathematics::Probability, Random time, 60G07, 0502 economics and business, enlargement of filtration, 60G44, Pricing of Securities (q-fin.PR), 0101 mathematics, Statistics, Probability and Uncertainty, Quantitative Finance - Pricing of Securities
Abstract: On a probability space $(\Omega,\mathcal{A},\mathbb{Q})$ we consider two filtrations $\mathbb{F}\subset \mathbb{G}$ and a $\mathbb{G}$ stopping time $\theta$ such that the $\mathbb{G}$ predictable processes coincide with $\mathbb{F}$ predictable processes on $(0,\theta]$. In this setup it is well-known that, for any $\mathbb{F}$ semimartingale $X$, the process $X^{\theta-}$ ($X$ stopped ``right before $\theta$'') is a $\mathbb{G}$ semimartingale.Given a positive constant $T$, we call $\theta$ an invariance time if there exists a probability measure $\mathbb{P}$ equivalent to $\mathbb{Q}$ on $\mathcal{F}_T$ such that, for any $(\mathbb{F},\mathbb{P})$ local martingale $X$, $X^{\theta-}$ is a $(\mathbb{G},\mathbb{Q})$ local martingale. We characterize invariance times in terms of the $(\mathbb{F},\mathbb{Q})$ Az\'ema supermartingale of $\theta$ and we derive a mild and tractable invariance time sufficiency condition. We discuss invariance times in mathematical finance and BSDE applications.
Published: 2017

30. Eigen-Epistasis for detecting Gene-Gene interactions

Author: Stanislas, Virginie, Dalmasso, Cyril, Ambroise, Christophe, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université d'Evry Val d'Essonne, Universite d'Evry Val d'Essonne, ENSIIE, INRA, CNRS [8071], Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, and Université d'Évry-Val-d'Essonne (UEVE)
Subjects: FOS: Computer and information sciences, Genome-wide association study, Genotype, [SDV]Life Sciences [q-bio], Polymorphism, Single Nucleotide, Statistics - Applications, Biochemistry, Genome Wide Association Study, Methodology (stat.ME), [STAT.AP] Statistics [stat]/Applications [stat.AP], Gene-gene interactions, Humans, Computer Simulation, Applications (stat.AP), Thyroid Neoplasms, Molecular Biology, Statistics - Methodology, Principal Component Analysis, [STAT.AP]Statistics [stat]/Applications [stat.AP], [STAT.ME] Statistics [stat]/Methodology [stat.ME], Methodology Article, Epistasis, Group Lasso, Computational Biology, Epistasis, Genetic, Models, Theoretical, Gene gene interactions, Inflammatory Bowel Diseases, Computer Science Applications, Phenotype, [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract: Background A large amount of research has been devoted to the detection and investigation of epistatic interactions in genome-wide association studies (GWASs). Most of the literature focuses on low-order interactions between single-nucleotide polymorphisms (SNPs) with significant main effects. Results In this paper we propose an original approach for detecting epistasis at the gene level, without systematically filtering on significant genes. We first compute interaction variables for each gene pair by finding its Eigen-Epistasis component, defined as the linear combination of Gene SNPs having the highest correlation with the phenotype. The selection of significant effects is done using a penalized regression method based on Group Lasso controlling the False Discovery Rate. Conclusion The method is tested against two recent alternative proposals from the literature using synthetic data, and shows good performances in different settings. We demonstrate the power of our approach by detecting new gene-gene interactions on three genome-wide association studies. Electronic supplementary material The online version of this article (doi:10.1186/s12859-017-1488-0) contains supplementary material, which is available to authorized users.
Published: 2017
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31. Central Clearing Valuation Adjustment

Author: Stéphane Crépey, Yannick Armenti, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), The research of Stéphane Crépey benefited from the support of the Chair Markets in Transition under the aegis of Louis Bachelier laboratory, a joint initiative of \'Ecole polytechnique, Université d'Evry Val d'Essonne and Fédération Bancaire Française, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)
Subjects: Total cost, counterparty risk, Computational Finance (q-fin.CP), margins, 01 natural sciences, [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], FOS: Economics and business, netting, 010104 statistics & probability, Quantitative Finance - Computational Finance, 0502 economics and business, Capital requirement, Econometrics, Clearing, Economics, 0101 mathematics, Valuation (finance), default fund, Finance, Numerical Analysis, 050208 finance, business.industry, Applied Mathematics, [QFIN.CP] Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], 05 social sciences, counterparty risk,cost of capital,central counterparty (CCP),margins,default fund,cost of funding,netting, Cost of capital, Risk Management (q-fin.RM), central counterparty (CCP), Default, cost of funding, Pricing of Securities (q-fin.PR), cost of capital, business, Quantitative Finance - Pricing of Securities, Clearance, Credit risk, Quantitative Finance - Risk Management
Abstract: This paper develops an XVA (costs) analysis of centrally cleared trading, parallel to the one that has been developed in the last years for bilateral transactions. We introduce a dynamic framework that incorporates the sequence of cash-flows involved in the waterfall of resources of a clearing house. The total cost of the clearance framework for a clearing member, called CCVA for central clearing valuation adjustment, is decomposed into a CVA corresponding to the cost of its losses on the default fund in case of defaults of other member, an MVA corresponding to the cost of funding its margins and a KVA corresponding to the cost of the regulatory capital and also of the capital at risk that the member implicitly provides to the CCP through its default fund contribution. In the end the structure of the XVA equations for bilateral and cleared portfolios is similar, but the input data to these equations are not the same, reflecting different financial network structures. The resulting XVA numbers differ, but, interestingly enough, they become comparable after scaling by a suitable netting ratio.
Published: 2017

32. SOME NO-ARBITRAGE RULES FOR CONVERGING ASSET PRICES UNDER SHORT-SALES CONSTRAINTS

Author: Coculescu, Delia, Jeanblanc, Monique, JEANBLANC, Monique, University of Zürich, Universität Zürich [Zürich] = University of Zurich (UZH), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), University of Zürich [Zürich] (UZH), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques et Modélisation d'Evry
Subjects: FOS: Economics and business, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Mathematics::Probability, Quantitative Finance - Mathematical Finance, Mathematics::Optimization and Control, Mathematical Finance (q-fin.MF)
Abstract: Under short sales prohibitions, no free lunch with vanishing risk (NFLVR-S) is known to be equivalent to the existence of an equivalent supermartingale measure for the price processes (Pulido [22]). For two given price processes, we translate the property (NFLVR-S) in terms of so called structure conditions and we introduce the concept of fundamental supermartingale measure. When a certain condition necessary to the construction of the fundamental martingale measure is not fulfilled, we provide the corresponding arbitrage portfolios. The motivation of our study lies in understanding the particular case of converging prices, i.e., that are going to cross at a bounded random time., Comment: 23 pages
Published: 2017

33. Weak Error for the Euler Scheme Approximation of Diffusions with Non-Smooth Coefficients *

Author: Valentin Konakov, Stéphane Menozzi, Higher School of Economics, National Research University, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), The article was prepared within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program., Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Hölder condition, Non smooth, 01 natural sciences, Euler Scheme, 010104 statistics & probability, non smooth coefficients, FOS: Mathematics, 65C30, Hölder coefficients, 0101 mathematics, Diffusion (business), Mathematics, Degenerate diffusion, Parametrix, 010102 general mathematics, Mathematical analysis, Probability (math.PR), diffusion processes, Piecewise smooth bounded drifts, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Weak Error, Bounded function, Piecewise, Euler scheme, 60H10, Statistics, Probability and Uncertainty, Mathematics - Probability
Abstract: We study the weak error associated with the Euler scheme of non degenerate diffusion processes with non smooth bounded coefficients. Namely, we consider the cases of H{\"o}lder continuous coefficients as well as piecewise smooth drifts with smooth diffusion matrices., Comment: 45 pages
Published: 2017

34. Asymptotics in small time for the density of a stochastic differential equation driven by a stable LEVY process

Author: Huong Nguyen, Emmanuelle Clément, Arnaud Gloter, Clément, Emmanuelle, Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec, Fédération de Mathématiques de l'Ecole Centrale Paris (FR3487), Ecole Centrale Paris-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université d'Évry-Val-d'Essonne (UEVE), Université Paris-Est Marne-la-Vallée (UPEM), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Ecole Centrale Paris, and ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, Work (thermodynamics), [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Lévy process, 010102 general mathematics, Mathematical analysis, Derivative, Conditional expectation, Malliavin calculus, 01 natural sciences, [STAT] Statistics [stat], Stable process, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [STAT]Statistics [stat], 010104 statistics & probability, Stochastic differential equation, Density in small time, Sensitivity (control systems), 0101 mathematics, [MATH]Mathematics [math], MSC2010 : 60G51, 60G52, 60H07, 60H20, 60H10, 60J75, Malliavin calculus for jump processes, Mathematics
Abstract: This work focuses on the asymptotic behavior of the density in small time of a stochastic differential equation driven by a truncatedα-stable process with indexα∈ (0, 2). We assume that the process depends on a parameterβ= (θ,σ)Tand we study the sensitivity of the density with respect to this parameter. This extends the results of [E. Clément and A. Gloter, Local asymptotic mixed normality property for discretely observed stochastic dierential equations driven by stable Lévy processes.Stochastic Process. Appl.125 (2015) 2316–2352.] which was restricted to the indexα∈ (1, 2) and considered only the sensitivity with respect to the drift coefficient. By using Malliavin calculus, we obtain the representation of the density and its derivative as an expectation and a conditional expectation. This permits to analyze the asymptotic behavior in small time of the density, using the time rescaling property of the stable process.
Published: 2017
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35. $L^$p Estimates For Degenerate Non-Local Kolmogorov Operators

Author: Huang, L., Menozzi, S., Priola, E., Michigan State University [East Lansing], Michigan State University System, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Higher School of Economics, National Research University, Dipartimento di Matematica 'Giuseppe Peano' [Torino], Università degli studi di Torino (UNITO), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Università degli studi di Torino = University of Turin (UNITO), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)
Subjects: Calderon-Zygmund estimates, L^p estimates, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Analysis of PDEs, Probability (math.PR), FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Degenerate non local operators, Mathematics - Probability, Analysis of PDEs (math.AP)
Abstract: Let $z = (x,y) \in {\mathbb R}^d \times {\mathbb R}^{N-d}$, with $1 \le d < N$. We prove a priori estimates of the following type :$$\|\Delta\_{x}^{\frac \alpha 2} v \|\_{L^p({\mathbb R}^N)} \lec\_p\Big \| L\_{x } v + \sum\_{i,j=1}^{N}a\_{ij}z\_{i}\partial\_{z\_{j}} v \Big \|\_{L^p({\mathbb R}^N)}, \;\; 1
Published: 2017
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36. Metamodel construction for sensitivity analysis

Author: Marie-Luce Taupin, Sylvie Huet, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de la Recherche Agronomique (INRA), Taupin, Marie-Luce, Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)
Subjects: T57-57.97, Statistics::Theory, Applied mathematics. Quantitative methods, Computer science, Gaussian, Hilbert space, Estimator, Mathematics - Statistics Theory, Regression analysis, Multivariate normal distribution, Statistics Theory (math.ST), Metamodeling, Statistics::Computation, symbols.namesake, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], QA1-939, symbols, FOS: Mathematics, Statistiques (Mathématiques), Sensitivity (control systems), [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Algorithm, Mathematics, Reproducing kernel Hilbert space
Abstract: We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse non-parametric estimation in multivariate Gaussian regression model. It rests on the construction of a metamodel for aproximating the Hoeffding-Sobol decomposition of m. This metamodel belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to a functional ANOVA decomposition. The estimation of the metamodel is carried out via a penalized least-squares minimization allowing to select the subsets of variables that contribute to predict the output. It allows to estimate the sensitivity indices of m. We establish an oracle-type inequality for the risk of the estimator, describe the procedure for estimating the metamodel and the sensitivity indices, and assess the performances of the procedure via a simulation study., Nous considérons l’estimation d’un méta-modèle d’un modèle complexe m à partir des observations d’un n-échantillon dans un modèle de régression gaussien. Nous en déduisons une estimation des indices de sensibilité de m. Notre approche combine les méthodes d’analyse de sensibilité de modèles complexes et les outils statistiques de l’estimation non-paramétrique en régression multivariée. Elle repose sur la construction d’un méta-modèle qui approche la décomposition de Hoeffding-Sobol de m. Ce méta-modèle appartient à un espace de Hilbert à noyau reproduisant qui est lui-même la somme directe d’espaces de Hilbert, permettant ainsi une décomposition de type ANOVA. On en déduit des estimateurs des indices de sensibilité de m. Nous établissons une inégalité de type oracle pour le risque de l’estimateur, nous décrivons la procédure pour estimer le méta-modèle et les indices de sensibilité, et évaluons les performances de notre méthode à l’aide d’une étude de simulations.
Published: 2017
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37. Continuous-time semi-markov inference of biometric laws associated with a long-term care insurance portfolio

Author: Guillaume Biessy, UMR1152 SG Statistique et Génome, USC1152 Laboratoire de Mathématiques Modélisation d'Evry, UMR8071 Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA), Centre National de la Recherche Scientifique (CNRS), Université d'Evry Val d'Essonne, SCOR Global Life SE, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), and Université d'Évry-Val-d'Essonne (UEVE)
Subjects: Economics and Econometrics, continuous-time semi-Markov process, [SDV]Life Sciences [q-bio], Inference, 01 natural sciences, 010104 statistics & probability, Accounting, 0502 economics and business, Econometrics, Economics, 0101 mathematics, Long-term care insurance, maximum likelihood, Parametric statistics, competing risks, mixture model, 050208 finance, Actuarial science, Markov chain, 05 social sciences, parametric model, Mixture model, Discrete time and continuous time, Law, Parametric model, Portfolio, Finance
Abstract: Unlike the mortality risk on which actuaries have been working for more than a century, the long-term care (LTC) risk is relatively new and as of today hardly mastered. Semi-Markov processes have been identified as an adequate tool to study this risk. Nevertheless, access to data is limited and the associated literature still scarce. Insurers mainly use discrete time methods directly inspired from the study of mortality in order to build experience tables. Those methods however are not perfectly suited for the study of competing risk situations. This article provides a theoretical framework to estimate biometric laws associated with a LTC insurance portfolio. The presented method relies on a continuous-time semi-Markov model with three states: autonomy, disability and death. The process describing the state of disability is defined through its transition intensities. We provide a formula to infer the mortality of autonomous people from the mortality of the whole portfolio, on which we have more reliable knowledge. We then propose a parametric expression for the remaining intensities of the model. In particular, incidence in LTC is described by a logistic formula. Under the assumption that the disabled population is a mixture of two latent populations with respect to the category of pathology that caused LTC, we show that the resulting intensity of mortality in LTC takes a very peculiar form and depends on time spent in the LTC state. Estimation of parameters relies on the maximum likelihood method. Our parametric approach, while inducing model uncertainty, eliminates issues related to segmentation in age categories, smoothing or extrapolation at higher ages and thus proves very convenient for the practitioner. Finally, we provide an application using data from a real LTC insurance portfolio.
Published: 2017
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38. The Brownian Motion on Aff(R) and Quasi-Local Theorems

Author: Konakov, V, Menozzi, S, Molchanov, Stanislav, Higher School of Economics, National Research University, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), University of North Carolina [Charlotte] (UNC), University of North Carolina System (UNC), The study has been funded by the Russian Science Foundation (project 17-11-01098), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Limit Theorems, Probability (math.PR), FOS: Mathematics, Mathematics - Probability, Random walks on groups
Abstract: This paper is concerned with Random walk approximations of the Brownian motion on the Affine group Aff(R). We are in particular interested in the case where the innovations are discrete. In this framework, the return probability of the walk have fractional exponential decay in large time, as opposed to the polynomial one of the continuous object. We prove that integrating those return probabilities on a suitable neighborhood of the origin, the expected polynomial decay is restored. This is what we call a Quasi-local theorem.
Published: 2017
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39. Collision of almost parallel vortex filaments

Author: Evelyne Miot, Valeria Banica, Erwan Faou, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Invariant Preserving SOlvers (IPSO), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-AGROCAMPUS OUEST-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques Laurent Schwartz (CMLS), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Inria Rennes – Bretagne Atlantique, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Département de Mathématiques [Evry], Université d'Évry-Val-d'Essonne (UEVE), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Laboratoire de Mathématiques et Modélisation d'Evry ( LaMME ), Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -ENSIIE-Centre National de la Recherche Scientifique ( CNRS ), Invariant Preserving SOlvers ( IPSO ), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique ( Inria ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Centre de Mathématiques Laurent Schwartz ( CMLS ), École polytechnique ( X ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques et Modélisation d'Evry, AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-AGROCAMPUS OUEST, Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique, Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), and Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)
Subjects: Physics, Work (thermodynamics), Applied Mathematics, General Mathematics, 010102 general mathematics, Collision, 01 natural sciences, Symmetry (physics), 010305 fluids & plasmas, Vortex, Classical mechanics, Circulation (fluid dynamics), [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Analysis of PDEs, 0103 physical sciences, Polygon, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Point (geometry), 0101 mathematics, Constant (mathematics), ComputingMilieux_MISCELLANEOUS, Analysis of PDEs (math.AP)
Abstract: We investigate the occurrence of collisions in the evolution of vortex filaments through a system introduced by Klein, Majda, and Damodaran and Zakharov . We first establish rigorously the existence of a pair of almost parallel vortex filaments, with opposite circulation, colliding at some point in finite time. The collision mechanism is based on one of the self-similar solutions of the model, described by the authors in an earlier work. In the second part of this paper we extend this construction to the case of an arbitrary number of filaments, with polygonal symmetry, that are perturbations of a configuration of parallel vortex filaments forming a polygon, with or without its center, rotating with constant angular velocity.© 2016 Wiley Periodicals, Inc.
Published: 2017
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40. Modeling heterogeneity in random graphs through latent space models: a selective review

Author: Stéphane Robin, Catherine Matias, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique Appliquées (MIA-Paris), AgroParisTech-Institut National de la Recherche Agronomique (INRA), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie - Paris 6 (UPMC) - Université Paris Diderot - Paris 7 (UP7) - Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - AgroParisTech, INRA, Institut National de la Recherche Agronomique (INRA), and Institut National de la Recherche Agronomique (INRA)-AgroParisTech
Subjects: FOS: Computer and information sciences, Méthodologie, Theoretical computer science, Computer science, Stochastic block model, Mathematics - Statistics Theory, Statistics Theory (math.ST), Space (mathematics), Methodology (stat.ME), Graph clustering, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, QA1-939, Statistiques (Mathématiques), [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Statistics - Methodology, Random graphs, Clustering coefficient, Block (data storage), Random graph, T57-57.97, [STAT.ME] Statistics [stat]/Methodology [stat.ME], Applied mathematics. Quantitative methods, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Methodology, Probabilistic logic, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [STAT.ME]Statistics [stat]/Methodology [stat.ME], Mathematics
Abstract: We present a selective review on probabilistic modeling of heterogeneity in random graphs. We focus on latent space models and more particularly on stochastic block models and their extensions that have undergone major developments in the last five years., Nous présentons une revue non exhaustive de la modélisation probabiliste de l'hétérogénéité des graphes aléatoires. Nous décrivons les modèles à espaces latents en nous intéressant plus particulièrement au modèle à blocs stochastiques et ses extensions, qui a connu des développements majeurs au cours des cinq dernières années.
Published: 2014
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41. Development of statistical methods for DNA copy number analysis in cancerology

Author: Pierre-Jean, Morgane, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université Paris Saclay, Pierre Neuvial (pierre.neuvial@genopole.cnrs.fr), C. Matias, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), and Pierre-Jean, Morgane
Subjects: [SDV.BIBS] Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], high dimension, Factorisation matricielle, matrix factorization, [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], DNA copy number, Cancérologie, tumoral heterogeneity, Segmentation, Nombre de copies d'ADN, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Grande dimension, [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Hétérogénéité tumorale, [INFO.INFO-BI] Computer Science [cs]/Bioinformatics [q-bio.QM], cancerology
Abstract: Genomic data from DNA microarray or sequencing technologies have two major characteristics: their high dimension (number of markers larger than the number of observations), and their strong structuration (dependence between markers). Taking into account this structuration, it is a challenging issue for the development of efficient methods. This work is focused on the data with a strong spatial structuration, namely DNA copy number data in tumor samples. We developed statistical models, software implementations and we applied these developments to real data. We explored in particular segmentation models and matrix factorization methods. All the software Implementations of these methods are freely available as R packages., Les données génomiques issues d'expériences de puces à ADN ou de séquençage ont deux caractéristiques principales: leur grande dimension (le nombre de marqueurs dépassant de plusieurs ordres de grandeurs le nombre d'observations), et leur forte structuration (notamment via les dépendances entre marqueurs). La prise en compte de cette structuration est un enjeu clé pour le développement de méthodes performantes en grande dimension. Cette thèse est axée sur les données présentant une forte structure le long du génome. C'est le cas des données de nombres de copies d'ADN, mais aussi des données de génotypes. La thèse couvre à la fois le développement de méthodes statistiques, l'implémentation logicielle, et l'application des méthodes développées à des jeux de données réelles. Nous avons, en particulier, étudié des méthodes de segmentation, et de factorisation matricielle. Toutes les implémentations logiciel de ces méthodes sont librement disponibles sous forme de packages R.
Published: 2016

42. Maximum likelihood estimator consistency for recurrent random walk in a parametric random environment with finite support

Author: Mikael Falconnet, Oleg Loukianov, Dasha Loukianova, Francis Comets, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université d'Évry-Val-d'Essonne (UEVE), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Université Pierre et Marie Curie - Paris 6 (UPMC) - Université Paris Diderot - Paris 7 (UP7) - Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS), Université Paris Diderot - Paris 7 (UPD7), and Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)
Subjects: Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Mathematical optimization, [SDV]Life Sciences [q-bio], 01 natural sciences, 010104 statistics & probability, FOS: Mathematics, Applied mathematics, 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Mathematics, Random walk in random environment, Heterogeneous random walk in one dimension, Recurrent regime, Estimation theory, Applied Mathematics, Probability (math.PR), 010102 general mathematics, Random function, Random element, Primary 62M05, 62F12, secondary 62F12, Maximum likelihood sequence estimation, Random walk, Maximum likelihood estimation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Random variate, Modeling and Simulation, Random variable, Mathematics - Probability
Abstract: International audience; We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood estimation procedure of the parameters of the environment. Unlike most of the classical maximum likelihood approach, the limit of the criterion function is in general a non degenerate random variable and convergence does not hold in probability. Not only the leading term but also the second order asymptotic is needed to fully identify the unknown parameter. We present different frameworks to illustrate these facts. We also explore the numerical performance of our estimation procedure.
Published: 2016
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43. Modélisation semi-markovienne de la perte d'autonomie chez les personnes âgées : application à l'assurance dépendance

Author: Biessy, Guillaume, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Thèse CIFRE, Université Paris-Saclay, Université d'Evry Val d'Essonne, Catherine Matias, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Biessy, Guillaume
Subjects: mixture model, [STAT.AP]Statistics [stat]/Applications [stat.AP], [STAT.AP] Statistics [stat]/Applications [stat.AP], Processus semi-markovien, local likelihood, censored data, données censurées, vraisemblance locale, modèle de mélange, semi-Markov process, assurance dépendance, Long-Term-Care Insurance
Abstract: Alongside the increase in life expectancy observed in developed countries since the beginningof the 20th century , numerous challenges arise for modern societies. Among them the loss ofautonomy in elderly people, also known as Long-Term Care (LTC). Long-term care may bedefined as a state of incapacity to perform autonomously part of the Activities of Daily Living(ADL). In most cases, long-term care is caused by one or several pathologies linked to aging.Disabled people therefore require help provided by a relative or professional caregiver or mayeven need to enter a nursing home. In France, a public aid called the Allocation Personnaliséepour l’Autonomie (APA), literally customized aid for autonomy, aims at covering the expensescaused by long-term care. Nevertheless, the amount of benefit is relatively small in regards ofthose expenses. Therefore, many insurers have designed products dedicated to complement thepublic aid.In order to price those products and monitor the risk, insurers need to model the long-termcare process. In most cases, one rely on multi-state modeling with states autonomy, death andone or several levels of LTC. To predict the risk one has to assess the transition probabilitiesbetween states. Under the Markov assumption, those probabilities are considered to onlydepend on the current state. As regards the study of LTC, this assumption may be seen as toorestrictive to account for the complexity of the underlying risk. In a semi-Markov framework,those probabilities may also depend on the time spent in the current state. In this thesis,we emphasis the necessity of the semi-Markov modeling. We demonstrate the impact of timespent in LTC on death probabilities. Besides, we exhibit that taking into account the diversityinduced by pathologies leads to sizable improvements in the fit of the model to experience data.Furthermore, we highlight that the peculiar shape taken by death probabilities as a function oftime spent in LTC may be explained by the mixture of pathology groups among the disabledpopulation.The first chapter of this thesis provides an introduction of the long-term care risk anddifferent tools to quantify it. The second chapter focuses on death probabilities among disabled,using the APA database. In the third chapter, we introduce a fully parametric approach toestimate transition probabilities in a model with a single state of LTC, relying on data froman insurance portfolio. Lastly, the fourth chapter study transition probabilities for 4 distinctgroups of pathologies: cancer, neurological diseases, dementia and other causes. This validatesthe empirical results obtained in the previous chapters., L’allongement de l’espérance de vie observé depuis le début du 20esiècle dans les paysindustrialisés pose un certain nombre de défis aux sociétés modernes. Parmi eux celui de laperte d’autonomie chez les personnes âgées, connue également sous le nom de dépendance. Ladépendance des personnes âgées se définit comme un état d’incapacité à effectuer seul toutou partie des Actes de la Vie Quotidienne (AVQ). La dépendance apparaît dans la grandemajorité des cas sous l’effet d’une ou plusieurs pathologies chroniques liées au vieillissement.Les personnes concernées ont alors besoin de l’assistance d’une tierce personne, un proche ou unaidant professionnel ou même d’intégrer un Établissement d’Hébergement pour Personnes ÂgéesDépendants (EHPAD) dans les cas les plus sévères. En France, une aide publique, l’AllocationPersonnalisée pour l’Autonomie (APA), est destinée à couvrir les frais liés à la dépendance.Cependant, le montant des prestations accordées demeure faible devant les dépenses engendrées.Aussi, de nombreux assureurs ont développé des produits spécifiques destinés à compléter l’aidepublique fournie par l’APA.Afin de fixer les prix de ces produits et d’assurer le suivi du risque, les assureurs ont besoinde modéliser le processus de dépendance. Cette modélisation passe dans la majorité des cas parune représentation multi-états du processus dont les états sont l’autonomie, le décès ainsi qu’unou plusieurs niveaux de dépendance. Pour prédire le risque il est alors nécessaire d’estimer lesprobabilités de transition entre ces états. Sous l’hypothèse de Markov, on considère que cesprobabilités de transition dépendent uniquement de l’état actuel. En ce qui concerne l’étude durisque de dépendance, cette hypothèse peut paraître trop restrictive pour rendre compte de lacomplexité du phénomène étudié. Dans le cadre semi-markovien, plus général, les probabilitésde transition peuvent également dépendre du temps passé dans l’état actuel. Au cours decette thèse, nous nous attachons à montrer la nécessité d’une modélisation semi-markoviennedu processus. Nous mettons ainsi en évidence l’impact du temps passé en dépendance surles probabilités de décès. Nous montrons par ailleurs que la prise en compte de la diversitéinduite par les pathologies permet d’améliorer sensiblement l’adéquation du modèle proposéaux données étudiées. Plus encore, nous établissons que la forme particulière de la probabilitéde décès en fonction du temps passé en dépendance peut être expliquée par le mélange desgroupes de pathologies qui constituent la population des individus dépendants.Le premier chapitre de la thèse propose une introduction du sujet et des principales méthodesutilisées pour sa quantification. Le deuxième chapitre est consacré à l’étude des probabilitésde transitions pour les individus déjà dépendants sur la base de données publiques de l’APA.Dans le troisième chapitre, nous introduisons une démarche entièrement paramétrique pourl’estimation des probabilités de transition dans un modèle avec un seul niveau de dépendancesur la base de données de portefeuilles. Nous prenons notamment en compte le rôle du mélangedes groupes de pathologies, quand bien même celles-ci ne sont pas observées. Enfin, lequatrième chapitre est consacré à l’étude des probabilités de transition associées à 4 groupesde pathologies : cancer, maladies neurologiques, démence et autres causes. Cette étude permetainsi de valider les résultats empiriques établis au cours des chapitres précédents.
Published: 2016

44. A theoretical study on the role of astrocytic activity in neuronal hyperexcitability by a novel neuron-glia mass model

Author: Garnier, Aurélie, Vidal, Alexandre, Benali, Habib, Laboratoire d'Imagerie Biomédicale [Paris] (LIB), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Labex SMART (ANR-11-LABX-65) supported by French state funds managed by the ANR within the Investissements d’Avenir programme under reference ANR-11-IDEX-0004-02, ANR-11-LABX-0065,SMART,Interactions humain/Machine/Humain intelligentes dans la société numérique(2011), ANR-11-IDEX-0004,SUPER,Sorbonne Universités à Paris pour l'Enseignement et la Recherche(2011), Laboratoire d'Imagerie Biomédicale (LIB), Laboratoire de Mathématiques et Modélisation d'Evry, ANR-11-LABX-0065,SMART,LabEX SMART(2011), ANR-11-IDEX-0004,SUPER(2011), Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), ANR: ANR-11-LABX-65,LabEX SMART, ANR-11-IDEX-0004-02/10-LABX-0065,LIFESENSES,DES SENS POUR TOUTE LA VIE(2011), and HAL UPMC, Gestionnaire
Subjects: Neuronal hyperexcitability, Research, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH] Mathematics [math], Qualitative analysis of dynamical systems, Bifurcations, nervous system, ODE Model in Neuroscience, MSC : 34C15, 34C23, 34C28, 34C46, 34C60, 34H20, 92C20, 92B25, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [SDV.NEU] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], Excitability modulation, [MATH]Mathematics [math], Neuron-astrocyte interactions, GABAergic and glutamatergic neurotransmissions
Abstract: International audience; Recent experimental evidence on the clustering of glutamate and GABA transporters on astrocytic processes surrounding synaptic terminals pose the question of the functional relevance of the astrocytes in the regulation of neural activity. In this perspective, we introduce a new computational model that embeds recent findings on neuron–astrocyte coupling at the mesoscopic scale intra- and inter-layer local neural circuits. The model consists of a mass model for the neural compartment and an astrocyte compartment which controls dynamics of extracellular glutamate and GABA concentrations. By arguments based on bifurcation theory, we use the model to study the impact of deficiency of astrocytic glutamate and GABA uptakes on neural activity. While deficient astrocytic GABA uptake naturally results in increased neuronal inhibition, which in turn results in a decreased neuronal firing, deficient glutamate uptake by astrocytes may either decrease or increase neuronal firing either transiently or permanently. Given the relevance of neuronal hyperexcitability (or lack thereof) in the brain pathophysiology, we provide biophysical conditions for the onset identifying different physiologically relevant regimes of operation for astrocytic uptake transporters.
Published: 2016
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45. Séminaire de Probabilités XLVIII

Author: Mathias Beiglböck, Martin Huesmann, Makoto Maejima, Nicolas Privault, Franck Maunoury, Anna Aksamit, Ismael Bailleul, Nicolas Juillet, David Applebaum, Christophe Profeta, Dai Taguchi, Peter Kern, Kilian Raschel, Alexis Devulder, Libo Li, Camille Tardif, Anita Behme, Thomas Simon, Gilles Pagès, Florian Stebegg, Oleskiy Khorunzhiy, Jürgen Angst, Stéphane Laurent, Cédric Lecouvey, Songzi Li, Wendelin Werner, Alexander Lindner, Matyas Barczy, Vienna University of Technology (TU Wien), Rheinische Friedrich-Wilhelms-Universität Bonn, Columbia University [New York], Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), TO Simulate and CAlibrate stochastic models (TOSCA), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institute of Mathematics [Debrecen], University of Debrecen Egyetem [Debrecen], Technische Universität Dresden = Dresden University of Technology (TU Dresden), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Nanyang Technological University [Singapour], Universität Ulm - Ulm University [Ulm, Allemagne], Keio University, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), North Dakota State University (NDSU), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Mathematical Institute [Oxford] (MI), University of Oxford, Université d'Évry-Val-d'Essonne (UEVE), School of Mathematics and Statistics [Sheffield] (SoMaS), University of Sheffield [Sheffield], Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), Donati-Martin, Catherine, Lejay, Antoine, Rouault, Alain, ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Technische Universität Wien (TU Wien), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), University of Debrecen, Technische Universität Dresden (TUD), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-AGROCAMPUS OUEST-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), University of Oxford [Oxford], Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology in Zürich [Zürich] (ETH Zürich), Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Université Pierre et Marie Curie - Paris 6 (UPMC), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Laboratoire de Mathématiques et Modélisation d'Evry, Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Technische Universität Wien ( TU Wien ), Bonn Universität [Bonn], Institut de Recherche Mathématique Avancée ( IRMA ), Université de Strasbourg ( UNISTRA ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Probabilités et Modèles Aléatoires ( LPMA ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Diderot - Paris 7 ( UPD7 ) -Centre National de la Recherche Scientifique ( CNRS ), TO Simulate and CAlibrate stochastic models ( TOSCA ), Inria Sophia Antipolis - Méditerranée ( CRISAM ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut Élie Cartan de Lorraine ( IECL ), Université de Lorraine ( UL ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Lorraine ( UL ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques de Versailles ( LMV ), Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ) -Université de Versailles Saint-Quentin-en-Yvelines ( UVSQ ), Technische Universität Dresden ( TUD ), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Universität Ulm, Laboratoire de Mathématiques et Physique Théorique ( LMPT ), Université de Tours-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques et Modélisation d'Evry ( LaMME ), Institut National de la Recherche Agronomique ( INRA ) -Université d'Évry-Val-d'Essonne ( UEVE ) -ENSIIE-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire Paul Painlevé - UMR 8524 ( LPP ), Université de Lille-Centre National de la Recherche Scientifique ( CNRS ), North Dakota State University ( NDSU ), Laboratoire Traitement et Communication de l'Information ( LTCI ), Télécom ParisTech, Institut Fourier ( IF ), Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), Mathematical Institute [Oxford] ( MI ), Université d'Évry-Val-d'Essonne ( UEVE ), School of Mathematics and Statistics [Sheffield] ( SoMaS ), and Eidgenössische Technische Hochschule [Zürich] ( ETH Zürich )
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2016
Full Text: View/download PDF

46. Recurrence relations for a family of generalized Cauchy numbers

Author: Chikhi, J, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), chikhi, jamel, Laboratoire de Mathématiques et Modélisation d'Evry, and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)
Subjects: recurrences, 11B83, 11B73, Bernoulli numbers of the second kind, [MATH] Mathematics [math], [MATH]Mathematics [math], generalized Cauchy numbers, Stirling numbers
Abstract: We obtain, for a two parameters family of generalized Cauchy numbers, two sorts of recurrence relations. The first recurrences are especially adapted to the so called shifted poly-Cauchy numbers. The second relations are generalization of the recurrences obtained by Agoh and Dilcher for the Bernoulli numbers of the second kind.
Published: 2016

47. INTEGRAL REPRESENTATION FOR SOME GENERALIZED POLY-CAUCHY NUMBERS

Author: Chikhi, J, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), and chikhi, jamel
Subjects: [MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract: In this note, we establish an integral representation for a special function E_{s,α} (z) and apply it to some generalized poly-Cauchy numbers c^(s)_{n,α} generated by the function E_{s,α} (log(1 + t)). We recover, in the special case α = s = 1, the integral representation of the Bernoulli numbers of the second kind obtained by Feng Qi by quite different methods.
Published: 2016

48. Local time penalizations with various clocks for one-dimensional diffusions

Author: Yuko Yano, Kouji Yano, Christophe Profeta, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, Kyoto University (Kyoto), Kyoto University [Kyoto], Kyoto Sangyo University, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), and Kyoto University
Subjects: one-dimensional diffusion, Diffusion (acoustics), penalization, General Mathematics, media_common.quotation_subject, 01 natural sciences, Measure (mathematics), Interpretation (model theory), 010104 statistics & probability, local time, 60F05, FOS: Mathematics, Applied mathematics, 60G44, Limit (mathematics), 0101 mathematics, 60J60, media_common, Mathematics, Probability (math.PR), excursion measure, 010102 general mathematics, Function (mathematics), Infinity, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Local time, Path (graph theory), Mathematics - Probability
Abstract: We study some limit theorems for the law of a generalized one-dimensional diffusion weighted and normalized by a non-negative function of the local time evaluated at a parametrized family of random times (which we will call a clock). As the clock tends to infinity, we show that the initial process converges towards a new penalized process, which generally depends on the chosen clock. However, unlike with deterministic clocks, no specific assumptions are needed on the resolvent of the diffusion. We then give a path interpretation of these penalized processes via some universal $ \sigma $-finite measures.
Published: 2016

49. New efficient algorithms for multiple change-point detection with kernels

Author: Celisse, Alain, Marot, Guillemette, Pierre-Jean, Morgane, Rigaill, Guillem, Université Lille Nord (France), Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), MOdel for Data Analysis and Learning (MODAL), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Santé publique : épidémiologie et qualité des soins-EA 2694 (CERIM), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Santé publique : épidémiologie et qualité des soins-EA 2694 (CERIM), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Unité de recherche en génomique végétale (URGV), Centre National de la Recherche Scientifique (CNRS)-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA), ANR-11-BS01-0010,Calibration,Calibration statistique(2011), Laboratoire Paul Painlevé (LPP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, and Laboratoire de Mathématiques et Modélisation d'Evry
Subjects: FOS: Computer and information sciences, dynamic programming, model selection, nonparametric change-point detection, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), algorithms, Statistics - Computation, DNA copy number, Kernel method, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Gram matrix, [STAT.CO]Statistics [stat]/Computation [stat.CO], Computation (stat.CO), allele B fraction
Abstract: Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good statistical properties (oracle inequality, \ldots). Nonetheless, they have a high computational cost both in terms of time and memory. This makes their application difficult even for small and medium sample sizes ($n< 10^4$). This computational issue is addressed by first describing a new efficient and exact algorithm for kernel multiple change-point detection with an improved worst-case complexity that is quadratic in time and linear in space. It allows dealing with medium size signals (up to $n \approx 10^5$). Second, a faster but approximation algorithm is described. It is based on a low-rank approximation to the Gram matrix. It is linear in time and space. This approximation algorithm can be applied to large-scale signals ($n \geq 10^6$). These exact and approximation algorithms have been implemented in \texttt{R} and \texttt{C} for various kernels. The computational and statistical performances of these new algorithms have been assessed through empirical experiments. The runtime of the new algorithms is observed to be faster than that of other considered procedures. Finally, simulations confirmed the higher statistical accuracy of kernel-based approaches to detect changes that are not only in the mean. These simulations also illustrate the flexibility of kernel-based approaches to analyze complex biological profiles made of DNA copy number and allele B frequencies. An R package implementing the approach will be made available on github.
Published: 2016

50. A semi-Markov model with pathologies for Long-Term Care Insurance

Author: Biessy, Guillaume, SCOR Global Life SE, Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), and Biessy, Guillaume
Subjects: [STAT.AP]Statistics [stat]/Applications [stat.AP], Long-Term Care Insurance, [STAT.AP] Statistics [stat]/Applications [stat.AP], [SDV.SPEE] Life Sciences [q-bio]/Santé publique et épidémiologie, local likelihood, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, continuous time semi-Markov process, competing risks
Abstract: Most Long-Term Care (LTC) Insurance products rely on definitions for functional disability based on the Activities of Daily Living (ADL). While functional disability may reflect the level of care required by the insured life, it is not on its own a good predictor of lifespan in LTC, which strongly depends on the underlying pathology responsible for disability. Indeed, cancer and respiratory diseases are associated with extremely short lifespan while dementia and neurological diseases make for much longer claims. Pathologies are therefore responsible for heterogeneity in the data, which makes estimation of mortality in LTC a difficult issue. As a consequence the associated literature is still scarce. In this paper, we study the mortality in LTC associated with 4 different groups of pathologies: cancer, dementia, neurological diseases and other causes based on data from a French LTC portfolio. We consider a semi-Markov framework, where mortality in LTC depends on both age at claim inception and time already spent in LTC. We first derive the incidence rate in LTC and mortality rate associated with each group of pathologies and for both males and females. To do so, we rely on local likelihood methods that we apply directly to transition intensities of the model. We then combine those transition intensities to get a second-step estimator of the overall mortality in LTC, which proves more accurate than a direct estimate regardless of the pathology. Finally our results indicates that the peak of mortality following entry in LTC observed in the data is mostly due to the cancer group.
Published: 2016

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