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We study the traditional backward Euler method for stochastic differential equation driven by fractional Brownian motion whose drift coefficient satisfies the one-sided Lipschitz condition. The backward Euler scheme is proved to be of order one and this rate is optimal by showing the asymptotic error distribution result. Numerical experiments are performed to validate our claims about the optimality of the rate of convergence. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence and uniqueness of the strong solution to one (spatial) dimensional stochastic wave equation ∂ 2 u (t , x) ∂ t 2 = ∂ 2 u (t , x) ∂ x 2 + σ (t , x , u (t , x)) W ˙ (t , x) assuming σ (t , x , 0) = 0 , where W ˙ is a mean zero Gaussian noise which is white in time and fractional in space with Hurst parameter H ∈ (1 / 4 , 1 / 2). [ABSTRACT FROM AUTHOR]

Serum ferritin (SF) is an iron-rich protein tightly connected with iron homeostasis, and the variations are frequently observed in diseased states, including iron-deficiency anemia, inflammation, liver disease, and tumors, which renders SF level an indicator of potential malignancies in clinical practice. Nanobodies (Nbs) have been widely explored and developed into theranostic reagents. Surprisingly, no reports stated the identification of anti-SF Nbs, nor the potential of such Nbs as a diagnostic tool. In this study, we generated SF-specific Nbs and provided novel clinical diagnostic approaches to develop an immunoassay. An immune library was constructed after immunizing an alpaca with SF, and five Nbs specifically targeting human SF were retrieved. The obtained Nbs exhibited robust properties including high stability, affinity, and specificity. Then, an ELISA-based test using a heterologous Nb-pair was developed. The calibration curve demonstrated a linear range of SF between 9.0 to 1100 ng/mL, and a limit of detection (LOD) of 1.01 ng/mL. The detecting recovery and coefficient variation (CV) were determined by spiking different concentrations of SF into the serum sample, to verify the successful application of our selected Nbs for SF monitoring. In general, this study generated SF-specific Nbs and demonstrated their potential as diagnostic immunoassay tools. [ABSTRACT FROM AUTHOR]

Trophoblast cell-surface antigen 2 (Trop-2) is a tumor-associated antigen that is connected with the development of various tumors and has been identified as a promising target for tumor immunotherapy. To date, the immunotherapy against Trop-2 mainly relies on the specific targeting by monoclonal antibody in antibody-drug conjugate (ADC). Alternatively, the single domain antibodies of nanobodies (Nbs) possesses unique properties such as smaller size, better tissue penetration, etc., to make them good candidates for tumor targeting. Thus, it was proposed to develop anti-Trop-2 Nbs for tumor targeting in this study. Generally, three consecutive rounds of bio-panning were performed against immobilized recombinant Trop-2, and yielded three Nbs (Nb60, Nb65, and Nb108). The affinity of selected Nbs was determined in the nanomolar range, especially the good properties of Nb60 were verified as a promising candidate for tumor labeling. The binding to native Trop-2 was confirmed by flow cytometry against tumor cells. The inhibitory effects of the selected Nbs on tumor cell proliferation and migration were confirmed by wound healing and Transwell assay. The clear localization of the selected Nbs on the surface of tumor cells verified the potent labeling efficiency. In conclusion, this study provided several Nbs with the potential to be developed as targeting moiety of drug conjugates. [ABSTRACT FROM AUTHOR]

In this paper, we study the stochastic differential equation with singular drift coefficient driven by fractional Brownian motion with Hurst parameter H ∈ (1 2 , 1). We obtain that the optimal convergence rate of the backward Euler method is 1.0. The constant elasticity of variance model and the Aït-Sahalia interest rate model are performed as numerical experiments to validate our theoretical results. [ABSTRACT FROM AUTHOR]

• Nanobody-based dual-mode immunoassay for Ara h 3 was developed with LOD of 6.61 ng/mL. • The dominance of nanobody and B/ N -CDs improved the accuracy of Ara h 3 immunoassay. • The method achieved the assessment of Ara h 3 in peanut contamination foodstuffs. To improve the performance of peanut allergen Ara h 3 detection, depending on boron and nitrogen carbon dots (B/ N -CDs), a nanobody (Nb) mediated dual-mode immunoassay was established, which combines the dominance of colorimetry with ratiometric fluorescence techniques. With the catalysis of Horseradish peroxidase (HRP), the oxidization of o-phenylenediamine (o-PD) in the presence of H 2 O 2 , leading to the production of yellow 2,3-diaminophenolazine (DAP) with an absorption peak at 431 nm. Owing to inner filter effect (IFE), DAP quenched the fluorescence of B/ N -CDs at 426 nm, and it emerged a new emission peak at 549 nm. The fluorescence intensity ratio and absorption intensity can be utilized for quantitative analysis of Ara h 3 concentration. Under optimal conditions, the detection limits were 6.61 and 9.79 ng·mL−1, respectively. The dual-mode immunoassay was assessed containing specificity, stability, reproducibility, and practicability. This method paved the way for sensitive detection of Ara h 3 without background Interference. [ABSTRACT FROM AUTHOR]

The goal of this paper is to construct ergodic estimators for double exponential Ornstein–Uhlenbeck process, where the process is observed at discrete time instants with time step size h. We show the existence and uniqueness of the function equations to determine the estimators for fixed time step size h. Also, we show the strong consistency and the asymptotic normality of the estimators. Furthermore, we propose a simulation method of the double exponential Ornstein–Uhlenbeck process and perform some numerical simulations to demonstrate the effectiveness of the proposed estimators. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of backward doubly stochastic differential equations (BDSDEs for short) with general terminal value and general random generator. Those BDSDEs do not involve any forward diffusion processes. By using the techniques of Malliavin calculus, we are able to establish the L p -Hölder continuity of the solution pair. Then, an implicit numerical scheme for the BDSDE is proposed and the rate of convergence is obtained in the L p -sense. As a by-product, we obtain an explicit representation of the process Y in the solution pair to a linear BDSDE with random coefficients. [ABSTRACT FROM AUTHOR]

We derive the strong consistency of the least squares estimator (LSE) for the drift coefficient of a fractional stochastic differential system. The drift coefficient is one-sided dissipative Lipschitz and the driving noise is additive and fractional with Hurst parameter H ∈ (1 4 , 1). We assume that continuous observation is possible. The main tools are ergodic theorem and Malliavin calculus. As a by-product, we derive a maximum inequality for Skorohod integrals, which plays an important role to obtain the strong consistency of the LSE. [ABSTRACT FROM AUTHOR]

This paper studies the nonlinear stochastic partial differential equation of fractional orders both in space and time variables: ∂ β + ν 2 (− Δ) α ∕ 2 u (t , x) = I t γ ρ (u (t , x)) W ̇ (t , x) , t > 0 , x ∈ R d , where W ̇ is the space–time white noise, α ∈ (0 , 2 ] , β ∈ (0 , 2) , γ ≥ 0 and ν > 0. Fundamental solutions and their properties, in particular the nonnegativity, are derived. The existence and uniqueness of solution together with the moment bounds of the solution are obtained under Dalang's condition: d < 2 α + α β min (2 γ − 1 , 0). In some cases, the initial data can be measures. When β ∈ (0 , 1 ] , we prove the sample path regularity of the solution. [ABSTRACT FROM AUTHOR]

The objective of this article is to introduce and study Itô type stochastic integrals with respect to tempered fractional Brownian motion (TFBM) of Hurst index H ∈ (1 2 , 1) and tempering parameter λ > 0 , by using the Wick product. The main tools are fractional calculus and Malliavin calculus. The Itô formula for this stochastic integral is established for the Itô type processes driven by TFBM. Based on this new Itô formula, we analyze the stability of stochastic differential equations driven by TFBM in the sense of p -th moment. A numerical example is given to illustrate our stability results. [ABSTRACT FROM AUTHOR]

• Our generator is a weighted fractional space-time Brownian field. • And it's not a backward martingale. • The existence, uniqueness and explicit solution pair for Y and Z. • Some kind of sharp Hlder continuity for the solution is obtained. • The Feynman-Kac Formula is established. This paper is concerned with the backward stochastic differential equations whose generator is a weighted fractional Brownian field: Y t = ξ + ∫ t T Y s W (d s , B s) − ∫ t T Z s d B s , 0 ≤ t ≤ T , where W is a (d + 1) -parameter weighted fractional Brownian field of Hurst parameter H = (H 0 , H 1 , ⋯ , H d) , which provide probabilistic interpretations (Feynman-Kac formulas) for certain linear stochastic partial differential equations with colored space-time noise. Conditions on the Hurst parameter H and on the decay rate of the weight are given to ensure the existence and uniqueness of the solution pair. Moreover, the explicit expression for both components Y and Z of the solution pair is given. [ABSTRACT FROM AUTHOR]

We study a pricing barrier control problem in a regime-switching regulated market. In doing so, we analyze a class of one-dimensional reflected regime-switching diffusion processes. Such diffusion models arise as the key approximating processes in a regulated financial market system with the presence of regime changes. Our main goal is to determine optimal pricing barriers as solutions of long-run average mean-variance optimization problems. More precisely, the optimal barrier, if exists, will be to maximize the long-run average expected return (i.e. steady-state mean) subject to a selected level of long-run average risk (i.e. steady-state variance). [ABSTRACT FROM AUTHOR]

Abstract We present an explicit solution triplet (Y , Z , K) to the backward stochastic Volterra integral equation (BSVIE) of linear type, driven by a Brownian motion and a compensated Poisson random measure. The process Y is expressed by an integral whose kernel is explicitly given. The processes Z and K are expressed by Hida–Malliavin derivatives involving Y. [ABSTRACT FROM AUTHOR]

This paper studies the existence and uniqueness of solution of Itô type stochastic differential equation , where B(t) is a fractional Brownian motion of Hurst parameter and is the Itô differential defined by using Wick product or divergence operator. The coefficients b and are random and anticipative. Using the relationship between the Itô and pathwise integrals we first write the equation as a stochastic differential equation involving pathwise integral plus a Malliavin derivative term. To handle this Malliavin derivative term the equation is then further reduced to a system of characteristic equations without Malliavin derivative, which is then solved by a careful analysis of Picard iteration, with a new technique to replace the Grönwall lemma which is no longer applicable. The solution of this system of characteristic equations is then applied to solve the original Itô stochastic differential equation up to a positive random time. In special linear and quasilinear cases the global solutions are proved to exist uniquely. [ABSTRACT FROM AUTHOR]

We propose a modified least squares estimator for the drift parameter of the Ornstein–Uhlenbeck process when the observations are available at a discrete instant in a low-frequency level. Unlike in the past literature, this modified least squares estimator is asymptotically unbiased. This estimator is combined with the ergodic theorem to obtain joint estimators ( θ ˆ n , σ ˆ n 2) for both drift and diffusion parameters (θ , σ 2). For any fixed observation time step h > 0 , the strong consistency and joint asymptotic normality of our estimators ( θ ˆ n , σ ˆ n 2) are obtained by using the linear model technology and the Delta method. Surprisingly, this linear model technology is not new but it is used for the first time to our model. It very significantly simplifies the arguments that researchers used in the literature. Numerical results illustrate the asymptotic behavior of the estimators. [ABSTRACT FROM AUTHOR]

This paper studies the stochastic heat equation driven by time fractional Gaussian noise with Hurst parameter H∈(0,1/2). We establish the Feynman-Kac representation of the solution and use this representation to obtain matching lower and upper bounds for the Lp(Ω) moments of the solution. [ABSTRACT FROM AUTHOR]

This article studies singular mean field control problems and singular mean field two-players stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some assumptions the optimality conditions for singular mean-field control are reduced to a reflected Skorohod problem, whose solution is proved to exist uniquely. Motivations are given as optimal harvesting of stochastic mean-field systems, optimal irreversible investments under uncertainty and mean-field singular investment games. In particular, a simple singular mean-field investment game is studied, where the Nash equilibrium exists but is not unique. [ABSTRACT FROM PUBLISHER]

The gene for a protein domain, derived from a tumor marker, fused to His tag codons and under control of a T7 promotor was expressed in E. coli strain BL21 (DE3). The recombinant protein was purified from cell lysates through immobilized metal affinity chromatography and size-exclusion chromatography. A contaminating bacterial protein was consistently co-purified, even using stringent washing solutions containing 50 or 100 mM imidazole. Immunization of a dromedary with this contaminated protein preparation, and the subsequent generation and panning of the immune Nanobody library yielded several Nanobodies of which 2/3 were directed against the bacterial contaminant, reflecting the immunodominance of this protein to steer the dromedary immune response. Affinity adsorption of this contaminant using one of our specific Nanobodies followed by mass spectrometry identified the bacterial contaminant as FKBP-type peptidyl-prolyl cis - trans isomerase (SlyD) from E. coli . This SlyD protein contains in its C-terminal region 14 histidines in a stretch of 31 amino acids, which explains its co-purification on Ni-NTA resin. This protein is most likely present to varying extents in all recombinant protein preparations after immobilized metal affinity chromatography. Using our SlyD-specific Nb 5 we generated an immune-complex that could be removed either by immunocapturing or by size exclusion chromatography. Both methods allow us to prepare a recombinant protein sample where the SlyD contaminant was quantitatively eliminated. [ABSTRACT FROM AUTHOR]

This paper studies the weak and strong solutions to the stochastic differential equation d X ( t ) = − 1 2 W ̇ ( X ( t ) ) d t + d B ( t ) , where ( B ( t ) , t ≥ 0 ) is a standard Brownian motion and W ( x ) is a two sided Brownian motion, independent of B . It is shown that the Itô–McKean representation associated with any Brownian motion (independent of W ) is a weak solution to the above equation. It is also shown that there exists a unique strong solution to the equation. Itô calculus for the solution is developed. For dealing with the singularity of drift term ∫ 0 T W ̇ ( X ( t ) ) d t , the main idea is to use the concept of local time together with the polygonal approximation W π . Some new results on the local time of Brownian motion needed in our proof are established. [ABSTRACT FROM AUTHOR]

In this paper, we study the mean square stability of the solution and its stochastic theta scheme for the following stochastic differential equations driven by fractional Brownian motion with Hurst parameter H ∈ (1 2 , 1) : d X (t) = f (t , X (t)) d t + g (t , X (t)) d B H (t). Firstly, we consider the special case when f (t , X) = − λ κ t κ − 1 X and g (t , X) = μ X. Secondly, the stability of the solution and its stochastic theta scheme for nonlinear equations is studied. Due to presence of long memory, even the problem of stability in the mean square sense of the solution has not been well studied, let alone the stability of numerical schemes. A complete new set of techniques to deal with this difficulty are developed. Numerical examples are carried out to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Assuming that a threshold Ornstein–Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. With the sampling time step arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sample size tends to infinity. [ABSTRACT FROM AUTHOR]

We consider a class of one-dimensional (1D) reflected stochastic differential equations (SDEs). Such reflected SDE models arise as the key approximating processes in a regulated financial market system, and our main goal is to determine the set of optimal pricing barriers. We consider the running cost associated with the deviation of the process from the desired target level, and also the control cost from the interventions in an effort to keep the process inside the boundaries. Both a long-time average (ergodic) cost criterion and an infinite horizon discount cost criterion, where the discount factor is allowed to vary from one period to another, are studied, with numerical examples illustrating our main results. [ABSTRACT FROM AUTHOR]

We prove a weak rate of convergence of a fully discrete scheme for stochastic Cahn–Hilliard equation with additive noise, where the spectral Galerkin method is used in space and the backward Euler method is used in time. Compared with the Allen–Cahn type stochastic partial differential equation, the error analysis here is much more sophisticated due to the presence of the unbounded operator in front of the nonlinear term. To address such issues, a novel and direct approach has been exploited which does not rely on a Kolmogorov equation but on the integration by parts formula from Malliavin calculus. To the best of our knowledge, the rates of weak convergence are revealed in the stochastic Cahn–Hilliard equation setting for the first time. [ABSTRACT FROM AUTHOR]

In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form (0.1) d Y (t) = − [ α 1 (t) Y (t) + β 1 (t) Z (t) + ∫ R 0 η 1 (t , ζ) K (t , ζ) ν (d ζ) + α 2 (t) E [ Y (t) ] + β 2 (t) E [ Z (t) ] + ∫ R 0 η 2 (t , ζ) E [ K (t , ζ) ] ν (d ζ) + γ (t) ] d t + Z (t) d B (t) + ∫ R 0 K (t , ζ) N ̃ (d t , d ζ) , t ∈ 0 , T , Y (T) = ξ. where (Y , Z , K) is the unknown solution triplet, B is a Brownian motion, N ̃ is a compensated Poisson random measure, independent of B. We prove the existence and uniqueness of the solution triplet (Y , Z , K) of such systems. Then we give an explicit formula for the first component Y (t) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Steinʼs method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed. [Copyright &y& Elsevier]

Multiple integrals with respect to several Hölder continuous functions of exponentare studied by using fractional calculus. They are applied to obtain the Volterra expansion (with remainder) for the solution of a differential system driven by rough paths. The results are applied to stochastic differential equations driven by fractional Brownian motions of Hurst parameter. For the solution of a stochastic differential equation driven by fractional Brownian motion, we obtain its chaos expansion, as well as the finite chaos expansion with remainder. To this end, we study the multiple Itô integral with random kernels. The Hu–Meyer formulas between multiple Itô and multiple pathwise integrals with random kernels are also obtained. [ABSTRACT FROM AUTHOR]

Abstract: We extend the classical Garsia–Rodemich–Rumsey inequality to the multiparameter situation. The new inequality is applied to obtain some joint Hölder continuity along the rectangles for fractional Brownian fields and for the solution of the stochastic heat equation with additive white noise. [Copyright &y& Elsevier]

Uncontrolled growth of solid tumors will result in a hallmark hypoxic condition, whereby the key transcriptional regulator of hypoxia inducible factor-1α (HIF-1α) will be stabilized to activate the transcription of target genes that are responsible for the metabolism, proliferation, and metastasis of tumor cells. Targeting and inhibiting the transcriptional activity of HIF-1 may provide an interesting strategy for cancer therapy. In the present study, an immune library and a synthetic library were constructed for the phage display selection of Nbs against recombinant PAS B domain protein (rPasB) of HIF-1α. After panning and screening, seven different nanobodies (Nbs) were selected, of which five were confirmed via immunoprecipitation to target the native HIF-1α subunit. The inhibitory effect of the selected Nbs on HIF-1 induced activation of target genes has been evaluated after intracellular expression of these Nbs in HeLa cells. The dramatic inhibition of both intrabody formats on the expression of HIF-1-related target genes has been confirmed, which indicated the inhibitory efficacy of selected Nbs on the transcriptional activity of HIF-1. [ABSTRACT FROM AUTHOR]

The Hölder continuity of the solution X( x) to a nonlinear stochastic partial differential equation (see (1.2) below) arising from one dimensional superprocesses is obtained. It is proved that the Hölder exponent in time variable is arbitrarily close to 1/4, improving the result of 1/10 in Li et al. (to appear on Probab. Theory Relat. Fields.). The method is to use the Malliavin calculus. The Hölder continuity in spatial variable x of exponent 1/2 is also obtained by using this new approach. This Hölder continuity result is sharp since the corresponding linear heat equation has the same Hölder continuity. [ABSTRACT FROM AUTHOR]

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need to develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we establish a version of the Feynman–Kac formula for multidimensional stochastic heat equation driven by a general semimartingale. This Feynman–Kac formula is then applied to study some nonlinear stochastic heat equations driven by nonhomogeneous Gaussian noise: first, an explicit expression for the Malliavin derivatives of the solutions is obtained. Based on the representation we obtain the smooth property of the density of the law of the solution. On the other hand, we also obtain the Hölder continuity of the solutions. [Copyright &y& Elsevier]

Abstract: We study the problem of parameter estimation for generalized Ornstein–Uhlenbeck processes driven by -stable noises, observed at discrete time instants. Least squares method is used to obtain an asymptotically consistent estimator. The strong consistency and the rate of convergence of the estimator have been studied. The estimator has a higher order of convergence in the general stable, non-Gaussian case than in the classical Gaussian case. [Copyright &y& Elsevier]

The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (0,1) in time. Two types of equations are considered. First we consider the equation in the Itô-Skorohod sense, and later in the Stratonovich sense. An explicit chaos expansion for the solution is obtained. On the other hand, the moments of the solution are expressed in terms of the exponential moments of some weighted intersection local time of the Brownian motion. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we apply Clark–Ocone formula to deduce an explicit integral representation for the renormalized self-intersection local time of the d-dimensional fractional Brownian motion with Hurst parameter . As a consequence, we derive the existence of some exponential moments for this random variable. [Copyright &y& Elsevier]

• The first report ever on nanobodies directed against intact S. aureus. • A Nb-mediated immuno-assay avoids false-positive detection of S. aureus. • Development of a sensitive sandwich ELISA against S. aureus. • The potential application to detect intact S. aureus in food matrix. The interaction between conventional immunoglobulins (Igs) and the Ig-binding surface proteins of Staphylococcus aureus (S. aureus) have obstructed the development of immuno-assays to detect these bacteria. The current study aimed to select nanobodies (Nbs) recognizing specifically S. aureus and to establish an immuno-assay to uncover S. aureus contaminations in foods. An alpaca was immunized with an inactivated S. aureus strain followed by the construction of a Nb library from which four target-specific Nbs were retrieved. Subsequently, a sandwich ELISA employing the Nb147 and biotinylated-Nb147 pair to capture and to detect S. aureus , respectively, was established to possess a detection limit of 1.4 × 105 colony forming units (CFU)/mL. The dedicated immuno-assay has been verified by detecting 10 CFU/mL of S. aureus in milk samples after an 8 h-enrichment step. This study provides the basis of an easy, reproducible and effective immuno-assay to screen for S. aureus contaminations in foods. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a fractional white noise calculus and to apply this to markets modeled by (Wick-) Itô type of stochastic differential equations driven by fractional Brownian motion B[SUBH](t); 1/2 < H < 1. We show that if we use an It&ocric; type of stochastic integration with respect to B[SUBH](t) (as developed in Ref. 8), then the corresponding It&ocric; fractional Black-Scholes market has no arbitrage, contrary to the situation when the pathwise integration is used. Moreover, we prove that our It&ocric; fractional Black-Scholes market is complete and we compute explicitly the price and replicating portfolio of a European option in this market. The results are compared to the classical results based on standard Brownian motion B(t). [ABSTRACT FROM AUTHOR]

We find the chaos expansion of local time ℓT(H)(x,·) of fractional Brownian motion with Hurst coefficient H∈(0,1) at a point x∈Rd. As an application we show that when H0d<1 then ℓT(H)(x,·)∈L2(μ). Here μ denotes the probability law of B(H) and H0=max{H1,…,Hd}. In particular, we show that when d=1 then ℓT(H)(x,·)∈L2(μ) for all H∈(0,1). [ABSTRACT FROM AUTHOR]

We prove a stochastic maximum principle for controlled processes X(t)=X(u)(t) of the formdX(t)=b(t,X(t),u(t)) dt+σ(t,X(t),u(t)) dB(H)(t),where B(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter H=(H1,…,Hm)∈(1/2,1)m. As an application we solve a problem about minimal variance hedging in an incomplete market driven by fractional Brownian motion. [Copyright &y& Elsevier]

The concept of probability structure preserving mapping is introduced. The idea is applied to define stochastic integral for fractional Brownian motion (fBm) and to obtain an anticipative Girsanov theorem for fBm. [Copyright &y& Elsevier]

In this paper we first establish the existence, uniqueness and Hölder continuity of the solution to stochastic Volterra integral equations (SVIEs) with weakly singular kernels, with singularities |$\alpha \in (0, 1)$| for the drift term and |$\beta \in (0, 1/2)$| for the stochastic term. Subsequently, we propose a |$\theta $| -Euler–Maruyama scheme and a Milstein scheme to solve the equations numerically and obtain strong rates of convergence for both schemes in |$L^{p}$| norm for any |$p\geqslant 1$|⁠. For the |$\theta $| -Euler–Maruyama scheme the rate is |$\min \big\{1-\alpha ,\frac{1}{2}-\beta \big\}~ $| and for the Milstein scheme is |$\min \{1-\alpha ,1-2\beta \}$|⁠. These results on the rates of convergence are significantly different from those it is similar schemes for the SVIEs with regular kernels. The source of the difficulty is the lack of Itô formula for the equations. To get around this difficulty we use the Taylor formula subsequently carrying out a sophisticated analysis of the equation. [ABSTRACT FROM AUTHOR]

Kernel methods are often used for nonlinear regression and classification in statistics and machine learning because they are computationally cheap and accurate. The wavelet kernel functions based on wavelet analysis can efficiently approximate any nonlinear functions. In this article, we construct a novel wavelet kernel function in terms of random wavelet bases and define a linear vector space that captures nonlinear structures in reproducing kernel Hilbert spaces (RKHS). Based on the wavelet transform, the data are mapped into a low-dimensional randomized feature space and convert kernel function into operations of a linear machine. We then propose a new Bayesian approximate kernel model with the random wavelet expansion and use the Gibbs sampler to compute the model's parameters. Finally, some simulation studies and two real datasets analyses are carried out to demonstrate that the proposed method displays good stability, prediction performance compared to some other existing methods. [ABSTRACT FROM AUTHOR]

An eight-degree-of-freedom vehicle dynamic model with electromechanical coupling was established for a four-wheel-independent-drive electric vehicle (4WID-EV). Based on the single-point preview optimal curvature theory, an adaptive fuzzy PID driver model with lateral acceleration feedback was designed, and the control of vehicle trajectory tracking was achieved in the driver-vehicle-road closed-loop coupling model. With the sideslip angle and yaw rate as control variables, the upper layer of a fuzzy sliding mode controller and the lower layer of an optimal distribution controller of the yaw moment were designed. The optimal longitudinal forces of four driving wheels were determined to achieve vehicle-handling stability. J-turn, fishhook, and snake-shaped pile simulations were carried out in MATLAB/Simulink. The results showed that the fuzzy sliding mode controller significantly improved the driving stability of the system, and it had a better anti-chattering ability than the sliding mode control strategy. The established lateral acceleration feedback adaptive fuzzy PID driver model had good trajectory tracking ability. Integration of the two controllers can better achieve both trajectory tracking and driving stability of a 4WID-EV. [ABSTRACT FROM AUTHOR]