Search

In heterogeneous treatment effect models with endogeneity, identification of the local average treatment effect (LATE) typically relies on the availability of an exogenous instrument monotonically related to treatment participation. First, we demonstrate that a strictly weaker local monotonicity condition—invoked for specific potential outcome values rather than globally—identifies the LATEs on compliers and defiers. Second, we show that our identification results apply to subsets of compliers and defiers when imposing an even weaker local compliers-defiers assumption that allows for both types at any potential outcome value. We propose estimators that are potentially more efficient than two-stage least squares (2SLS) in finite samples, even in cases where 2SLS is consistent. Finally, we provide an empirical application to estimating returns to education using the quarter of birth instrument. [ABSTRACT FROM AUTHOR]

This paper is devoted to proving the strong averaging principle for slow–fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally monotone coefficients and the fast component is a stochastic partial differential equations with strongly monotone coefficients. The result is applicable to a large class of examples, such as the stochastic porous medium equation, the stochastic p-Laplace equation, the stochastic Burgers type equation and the stochastic 2D Navier–Stokes equation, which are the nonlinear stochastic partial differential equations. The main techniques are based on time discretization and the variational approach to stochastic partial differential equations. [ABSTRACT FROM AUTHOR]

Lions in Lions (1969) solved the anisotropic p-Laplace equation in deterministic setting by considering the anisotropic p-Laplace operator in d-dimensions as a sum of d monotone coercive operators each defined on a different space. Motivated by this example, we prove existence and uniqueness results for a large class of stochastic partial differential equations(SPDEs) driven by Lévy noise when the operator appearing in the bounded variation term is a sum of operators having different analytic and growth properties. Further, the operators are allowed to be locally monotone without explicitly restricting the growth of the operators appearing in the stochastic integrals. This has been done by identifying an appropriate coercivity condition. As a consequence, well-posedness of Lévy driven stochastic Anisotropic p-Laplace equation has been shown. Our framework is most general till date. Many popular SPDEs appearing in real world models such as the stochastic Ginzburg–Landau equation and stochastic Swift–Hohenberg equation, both driven by Lévy noise, fit in our setting. These equations are not covered by the corresponding results in the literature. [ABSTRACT FROM AUTHOR]

Higher moment a priori estimates for solutions to nonlinear SPDEs governed by locally-monotone operators are obtained under appropriate coercivity condition. These are then used to extend known existence and uniqueness results for nonlinear SPDEs under local monotonicity conditions to allow derivatives in the operator acting on the solution under the stochastic integral. [ABSTRACT FROM AUTHOR]

In this work, we consider the three-dimensional viscoelastic fluid flow equations, arising from the motion of Kelvin-Voigt fluids in bounded and unbounded domains. We investigate the global solvability results, asymptotic behavior and also address some control problems of such viscoelastic fluid flow equations with "fading memory" and "memory of length τ". A local monotonicity property of the linear and nonlinear operators and a localized version of the Minty-Browder technique are used to obtain global solvability results. Since we are not using compactness arguments in the proofs, the global solvability results are also valid in unbounded domains like Poincaré domains. We also remark that using an m-accretive quantization of the linear and nonlinear operators, one can establish the existence and uniqueness of strong solutions for the Navier-Stokes-Voigt equations and avoid the tedious Galerkin approximation scheme. We examine the asymptotic behavior of the stationary solutions and also establish the exponential stability results. Finally, under suitable assumptions on the Galerkin basis, we consider the controlled Galerkin approximated 3D Kelvin-Voigt fluid flow equations. Using the Hilbert uniqueness method combined with Schauder's fixed point theorem, the exact controllability of the finite dimensional Galerkin approximated system is established. [ABSTRACT FROM AUTHOR]

We establish a local monotonicity identity for vector bundle-valued differential k-forms on superlevel sets of appropriate heat kernel-like functions. As a consequence, we obtain new local monotonicity formulæ for the harmonic map and Yang–Mills heat flows on evolving manifolds. We also show how these methods yield local monotonicity formulæ for the Yang–Mills–Higgs flow. [ABSTRACT FROM AUTHOR]

Abstract In this paper we present the Wong–Zakai approximation results for a class of nonlinear SPDEs with locally monotone coefficients and driven by multiplicative Wiener noise. This model extends the classical monotone one and includes examples like stochastic 2d Navier–Stokes equations, stochastic porous medium equations, stochastic p -Laplace equations and stochastic reaction–diffusion equations. As a corollary, our approximation results also describe the support of the distribution of solutions. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of strong solutions for stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity, and time delay. Our results extend previous results obtained by Liu–Röckner, Caraballo et al. and Taniguchi et al. Examples are given to illustrate the wide applicability of our results. [ABSTRACT FROM PUBLISHER]

This paper introduces and characterizes new notions of Lipschitzian and H?olderian full stability of solutions to general parametric variational systems defined via partial subdifferential of prox-regular functions acting in finite-dimensional and Hilbert spaces. These notions, which postulate certain quantitative properties of single-valued localizations of solution maps, are closely related to local strong maximal monotonicity of associated set-valued mappings. Based on advanced tools of variational analysis and generalized differentiation, we derive verifiable characterizations of the local strong maximal monotonicity and full stability notions under consideration via some positive-definiteness conditions involving second-order constructions of variational analysis. [ABSTRACT FROM AUTHOR]

In this work we establish the local solvability of quasilinear symmetric hyperbolic system using local monotonicity method and frequency truncation method. The existence of an optimal control is also proved as an application of these methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions, which can be applied to a large class of SPDE with finite delays, e.g. d -dimensional stochastic fractional Navier–Stokes equations with delays, d -dimensional stochastic reaction–diffusion equations with delays, d -dimensional stochastic porous media equations with delays. Moreover, under local monotonicity conditions for the nonlinear terms we obtain the existence and uniqueness of strong solutions to SPDE with delays. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we show the existence and uniqueness of strong solutions for a large class of SPDE where the coefficients satisfy the local monotonicity and Lyapunov condition (one-sided linear growth condition). Moreover, some new invariance result and stronger regularity estimate are also established for the solutions. As examples, the main result is applied to stochastic tamed 3D Navier–Stokes equations, stochastic generalized curve shortening flow, singular stochastic p-Laplace equations, stochastic fast diffusion equations, stochastic Burgers type equations and stochastic reaction–diffusion equations. [Copyright &y& Elsevier]

Abstract: We introduce a new simple game, which is referred to as the complementary weighted multiple majority game (C-WMMG for short). C-WMMG models a basic cooperation rule, the complementary cooperation rule, and can be taken as a sister model of the famous weighted majority game (WMG for short). In C-WMMG, each player is characterized by a nonnegative vector with a fixed dimension, and players in the same coalition cooperate by producing a characteristic vector for this coalition (each dimension of this vector equals the maximum of the corresponding dimensions of its members). The value of a coalition is 1 if and only if the sum of its characteristic vector is larger than that of its complementary coalition, in which case the coalition is called winning. Otherwise, the coalitional value is 0. In this paper, we concentrate on the two dimensional C-WMMG. An interesting property of this case is that there are at most minimal winning coalitions (MWCs for short), and they can be enumerated in time , where is the number of players. This property guarantees that the two dimensional C-WMMG is more handleable than WMG. In particular, we prove that the main power indices, i.e. the Shapley–Shubik index, the Penrose–Banzhaf index, the Holler–Packel index, and the Deegan–Packel index, are all polynomially computable. To make a comparison with WMG, we know that it may have exponentially many MWCs, and none of the four power indices is polynomially computable (unless ). Still for the two dimensional case, we show that local monotonicity holds for all of the four power indices. In WMG, this property is possessed by the Shapley–Shubik index and the Penrose–Banzhaf index, but not by the Holler–Packel index or the Deegan–Packel index. Since our model fits very well the cooperation and competition in team sports, we hope that it can be potentially applied in measuring the values of players in team sports, say help people give more objective ranking of NBA players and select MVPs, and consequently bring new insights into contest theory and the more general field of sports economics. It may also provide some interesting enlightenments into the design of non-additive voting mechanisms. Last but not least, the threshold version of C-WMMG is a generalization of WMG, and natural variants of it are closely related with the famous airport game and the stable marriage/roommates problem. [Copyright &y& Elsevier]

Abstract: In this paper we establish the local and global existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions. An analogous result is obtained for stochastic evolution equations in Hilbert space with additive noise. As applications, the main results are applied to obtain simpler proofs in known cases as the stochastic 3D Navier–Stokes equation, the tamed 3D Navier–Stokes equation and the Cahn–Hilliard equation, but also to get new results for stochastic surface growth PDE and stochastic power law fluids. [Copyright &y& Elsevier]

Abstract: We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is -locally monotone if none of its partial derivatives changes in sign on tuples which differ in less than positions. As it turns out, this parameterized notion provides a hierarchy of monotonicities for pseudo-Boolean (Boolean) functions. Local monotonicities are shown to be tightly related to lattice counterparts of classical partial derivatives via the notion of permutable derivatives. More precisely, -locally monotone functions are shown to have -permutable lattice derivatives and, in the case of symmetric functions, these two notions coincide. We provide further results relating these two notions, and present a classification of -locally monotone functions, as well as of functions having -permutable derivatives, in terms of certain forbidden “sections”, i.e., functions which can be obtained by substituting constants for variables. This description is made explicit in the special case when . [Copyright &y& Elsevier]

In this work we prove the existence and uniqueness of the strong solution of the shell model of turbulence perturbed by Lévy noise. The local monotonicity arguments have been exploited in the proofs. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the spreading speeds and traveling wavefronts of second order integrodifference equations with local monotonicity. By introducing two auxiliary integrodifference equations, the spreading speed and traveling wave solutions are studied. In particular, we obtain the nonexistence of monotone traveling wave solutions for an example if it is local monotone. These results are applied to a model which is obtained by introducing the spatial variable to a difference equation used by the International Whaling Commission. [Copyright &y& Elsevier]

Block-matching algorithms, such as TSS and DSWA/IS, are widely used for motion estimation in low-bit-rate video coding. The assumption behind these algorithms is that when the matching block moves away from the optimal block, the difference between them increases monotonically. Unfortunately, this assumption is often invalid, and therefore leads to a high possibility for the result to be trapped to local minima. In this research, we propose a new multiple-candidate search scheme, Hilbert scanning search algorithm (HSSA), in which the assumption of global monotonicity is not necessary and the local monotonicity can be effectively explored with binary search around each candidate. In HSSA, the number of initial candidates and a threshold to control the selection of candidates from one stage to the next can be adjusted to meet the required search accuracy and/or speed. With properly chosen parameters, the HSSA converges to their optimal results faster and with better accuracy than the conventional block-matching algorithms [ABSTRACT FROM PUBLISHER]

Key performance indicators (KPIs) are time series with the format of (timestamp, value). The accuracy of KPIs anomaly detection is far beyond our initial expectations sometimes. The reasons include the unbalanced distribution between the normal data and the anomalies as well as the existence of many different types of the KPIs data curves. In this paper, we propose a new anomaly detection model based on mining six local data features as the input of back-propagation (BP) neural network. By means of vectorization description on a normalized dataset innovatively, the local geometric characteristics of one time series curve could be well described in a precise mathematical way. Differing from some traditional statistics data characteristics describing the entire variation situation of one sequence, the six mined local data features give a subtle insight of local dynamics by describing the local monotonicity, the local convexity/concavity, the local inflection property and peaks distribution of one KPI time series. In order to demonstrate the validity of the proposed model, we applied our method on 14 classical KPIs time series datasets. Numerical results show that the new given scheme achieves an average F1-score over 90%. Comparison results show that the proposed model detects the anomaly more precisely. [ABSTRACT FROM AUTHOR]