scispace - formally typeset
Search or ask a question

Showing papers in "Stochastic Analysis and Applications in 2019"


Journal ArticleDOI
TL;DR: In this article, the global asymptotic stability of random impulsive coupled systems on networks with Markovian switching was studied, and two cases were considered: (1) continuous dy...
Abstract: This article is intended to study global asymptotical stability in probability for random impulsive coupled systems on networks with Markovian switching. Two cases are considered. (1) Continuous dy...

52 citations


Journal ArticleDOI
TL;DR: In this paper, the numerical solution of fractional stochastic delay differential equations driven by Brownian motion was studied, based on linear B-spline interpolation, and the proposed algorithm was shown to be robust to noise.
Abstract: This paper studies the numerical solution of fractional stochastic delay differential equations driven by Brownian motion. The proposed algorithm is based on linear B-spline interpolation. ...

34 citations


Journal ArticleDOI
TL;DR: In this paper, the MFG limit for interacting agents with a common noise was formulated as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation, which was proved to be correct.
Abstract: We formulate the MFG limit for N interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove tha...

32 citations


Journal ArticleDOI
Nacira Agram1
TL;DR: In this paper, the authors studied dynamic risk measures by means of backward backward regression, which is a fundamental concept in finance and in the insurance industry and is used to adjust life insurance rates.
Abstract: Risk measure is a fundamental concept in finance and in the insurance industry. It is used to adjust life insurance rates. In this article, we will study dynamic risk measures by means of backward ...

29 citations


Journal ArticleDOI
TL;DR: In this article, a class of impulsive Hilfer fractional stochastic differential systems driven by Rosenblatt process with index H∈(12,1) was investigated. And a special case of a self-similar proces was considered.
Abstract: This manuscript investigates a class of impulsive Hilfer fractional stochastic differential system driven by Rosenblatt process with index H∈(12,1), which is a special case of a self-similar proces...

23 citations


Journal ArticleDOI
TL;DR: In this article, the mild solution to fractional neutral stochastic integro-differential systems with state dependent delay and noninstantaneous impulses in HPC was studied.
Abstract: In this paper, we provide a framework for study the mild solution to fractional neutral stochastic integro-differential systems with state dependent delay and noninstantaneous impulses in H...

19 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the system becomes chaotic as the number of particles goes to infinity together with the time, under easily checked assumptions that the external force is not convex, with a diffusion coefficient sufficiently large.
Abstract: We are interested in nonlinear diffusions in which the own law intervenes in the drift. This kind of diffusions corresponds to the hydrodynamical limit of some particle system. One also talks about propagation of chaos. It is well-known, for McKean-Vlasov diffusions, that such a propagation of chaos holds on finite-time interval. However, it has been proven that the lack of convexity of the external force implies that there is no uniform propagation of chaos if the diffusion coefficient is small enough. We here aim to establish a uniform propagation of chaos even if the external force is not convex, with a diffusion coefficient sufficiently large. The idea consists in combining the propagation of chaos on a finite-time interval with a functional inequality, already used by Bolley, Gentil and Guillin, see \cite{BGG1,BGG2}. Here, we also deal with a case in which the system at time $t=0$ is not chaotic and we show under easily checked assumptions that the system becomes chaotic as the number of particles goes to infinity together with the time. This yields the first result of this type for mean field particle diffusion models as far as we know.

18 citations


Journal ArticleDOI
TL;DR: In this article, a stochastic one-prey two-predator model with Holling type II functional response was investigated and sufficient conditions for persistence and extinction of prey were established.
Abstract: In this article, we investigate a stochastic one-prey two-predator model with Holling type II functional response. We first establish sufficient conditions for persistence and extinction of prey an...

17 citations


Journal ArticleDOI
TL;DR: In this article, a class of mean field stochastic differential equations driven by fractional Brownian motion with Hurst parameter H∈(1/2,1) was studied.
Abstract: This paper concerns a class of mean field stochastic differential equations driven by fractional Brownian motion with Hurst parameter H∈(1/2,1). The existence and uniqueness of almost automorphic s...

15 citations


Journal ArticleDOI
TL;DR: In this paper, the asymptotic behavior of solutions for a nonlinear Marcus stochastic differential equation with multiplicative two-sided Levy noise is studied, and the authors consider the problem of finding the optimal solution to the problem.
Abstract: In this paper, the asymptotic behavior of solutions for a nonlinear Marcus stochastic differential equation with multiplicative two-sided Levy noise is studied. We plan to consider this equ...

14 citations


Journal ArticleDOI
TL;DR: The classical Picard theorem for deterministic ordinary differential equations is extended to calculus for random differential equations with delay, via Banach fixed-point theorem, and solutions with sample-path solutions are related.
Abstract: In this article, we study random differential equations with discrete delay τ>0: x′(t,ω)=f(x(t,ω),x(t−τ,ω),t,ω),t≥t0, with initial condition x(t,ω)=g(t,ω),t∈[t0−τ,t0]. The uncertainty in the proble...

Journal ArticleDOI
TL;DR: In this article, the spread of crime in a population is very much dependent on the social structure of the society, and there are several factors which influence the dynamics of the dynamics.
Abstract: Crime is a social epidemic. The spread of crime in a population is very much dependent on the social structure of the society. Although there are several factors which influence the dynamics of the...

Journal ArticleDOI
TL;DR: In many cases, the existence and uniqueness of the solution of a differential equation are proved using fixed point theory as mentioned in this paper, and in this paper, we utilize the theory of operators and ingenious t...
Abstract: In many cases, the existence and uniqueness of the solution of a differential equation are proved using fixed point theory. In this paper, we utilize the theory of operators and ingenious t...

Journal ArticleDOI
TL;DR: A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation.
Abstract: In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A...

Journal ArticleDOI
TL;DR: In this article, a variational calculus is presented to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions, combining gradient flow estimates with backward stochastic interpolations, Lyapunov linearization techniques as well as spectral theory.
Abstract: The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward stochastic interpolations, Lyapunov linearization techniques as well as spectral theory. This framework applies to a large class of stochastic models including non homogeneous diffusions, as well as stochastic processes evolving on differentiable manifolds, such as constraint-type embedded manifolds on Euclidian spaces and manifolds equipped with some Riemannian metric. We derive uniform as well as almost sure exponential contraction inequalities at the level of the nonlinear diffusion flow, yielding what seems to be the first result of this type for this class of models. Uniform propagation of chaos properties w.r.t. the time parameter are also provided. Illustrations are provided in the context of a class of gradient flow diffusions arising in fluid mechanics and granular media literature. The extended versions of these nonlinear Langevin-type diffusions on Riemannian manifolds are also discussed.

Journal ArticleDOI
TL;DR: In this paper, the distribution of the sum of independent Mittag-Leffler (ML) random variables which are not necessarily identically distributed is obtained, and the corresponding known result is discussed.
Abstract: We obtain the distribution of the sum of independent Mittag–Leffler (ML) random variables which are not necessarily identically distributed. Firstly we discuss the corresponding known result for in...

Journal ArticleDOI
TL;DR: In this article, the authors study non-homogeneous versions of the space-fractional and the time-frractional Poisson processes, which can be defined by means of the so-called multistable subordinator (a jump process with non-stationary increments), denoted by H. The authors consider the Poisson process time-changed by H and obtain its explicit distribution and governing equation.
Abstract: The space-fractional and the time-fractional Poisson processes are two well-known models of fractional evolution. They can be constructed as standard Poisson processes with the time variable replaced by a stable subordinator and its inverse, respectively. The aim of this paper is to study non-homogeneous versions of such models, which can be defined by means of the so-called multistable subordinator (a jump process with non-stationary increments), denoted by H. Firstly, we consider the Poisson process time-changed by H and we obtain its explicit distribution and governing equation. Then, by using the right-continuous inverse of H, we define an inhomogeneous analogue of the time-fractional Poisson process.

Journal ArticleDOI
TL;DR: In this article, the inverse first-passage time (IFPT) problem was revisited in the case of fractional Brownian motion and time-changed Brownian motions.
Abstract: We revisit an inverse first-passage time (IFPT) problem, in the cases of fractional Brownian motion, and time-changed Brownian motion. Let X(t) be a one dimensional continuous stochastic pr...

Journal ArticleDOI
TL;DR: The space-time fractional Poisson process (STFPP) as mentioned in this paper is a generalization of the TFPP and the space fractional poisson process, defined by Orsingher and Poilto (2012).
Abstract: The space-time fractional Poisson process (STFPP), defined by Orsingher and Poilto (2012), is a generalization of the time fractional Poisson process (TFPP) and the space fractional Poisson...

Journal ArticleDOI
TL;DR: In this article, the Markov chain has a countable state space and Markov switching is allowed in the state space, which is a novelty in the Lotka-Volterra model.
Abstract: This work is concerned with competitive Lotka–Volterra model with Markov switching A novelty of the contribution is that the Markov chain has a countable state space Our main objective of the pap

Journal ArticleDOI
TL;DR: In this article, the authors analyze a chemostat model with wall growth where the input flow is perturbed by two different stochastic processes: the standard Wiener process, which leads into severa...
Abstract: In this paper, we analyze a chemostat model with wall growth where the input flow is perturbed by two different stochastic processes: the well-known standard Wiener process, which leads into severa...

Journal ArticleDOI
TL;DR: In this article, the dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Levy jumps is considered, and a standard geometric Brownian motion and another two driving proce...
Abstract: In this paper, the dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Levy jumps is considered. Besides a standard geometric Brownian motion, another two driving proce...

Journal ArticleDOI
TL;DR: In this paper, the authors derive expressions for conditional expectations in terms of regular expectations without conditioning but involving some weights, and apply these expressions for the numerical estimation of the price of American options and their deltas in a Levy and jump-diffusion setting.
Abstract: In this article, we derive expressions for conditional expectations in terms of regular expectations without conditioning but involving some weights. For this purpose, we apply two approaches: the conditional density method and the Malliavin method. We use these expressions for the numerical estimation of the price of American options and their deltas in a Levy and jump-diffusion setting. Several examples of applications to financial and energy markets are given including numerical examples.

Journal ArticleDOI
TL;DR: In this article, some selection theorems for set-valued stochastic integrals considered in papers by Kisielewicz et al. are considered. But none of them are considered in this paper.
Abstract: The paper is devoted to some selection theorems for set-valued stochastic integrals considered in papers by Kisielewicz et al. In particular, the Ito set-valued stochastic integrals are considered ...

Journal ArticleDOI
TL;DR: In this paper, the Caratheodory approximate solution for a class of one-dimensional perturbed stochastic differential equations with reflecting boundary (PSDERB) is studied.
Abstract: In this work, we study the Caratheodory approximate solution for a class of one-dimensional perturbed stochastic differential equations with reflecting boundary (PSDERB). Based on the Caratheodory ...

Journal ArticleDOI
TL;DR: In this article, the Hermite-Hadamard inequality via pseudo-fractional integral of order α>0 in two classes of semiring (a,b, b, c, c) was given.
Abstract: In this paper, we give new versions of Hermite–Hadamard inequality via pseudo-fractional integral of order α>0 in two classes of semiring ([a,b],⊕,⊙). We show that if pseudo operations are ...

Journal ArticleDOI
TL;DR: In this paper, the existence of a unique invariant measure in case the forcing terms consist of the cylindrical Wiener processes with only low modes is proved, which is extended to various other related models such as the magnetohydrodynamics-Boussinesq system from fluid mechanics in atmosphere and oceans, as well as magneto-micropolar fluid system from the theory of microfluids.
Abstract: The magnetohydrodynamics system consists of the Navier-Stokes equations from fluid mechanics, coupled with the Maxwell’s equations from electromagnetism through multiples of non-linear terms involving derivatives. Following the approach of [1], we prove the existence of a unique invariant measure in case the forcing terms consist of the cylindrical Wiener processes with only low modes. Its proof requires taking advantage of the structure of the non-linear terms carefully and is extended to various other related models such as the magnetohydrodynamics-Boussinesq system from fluid mechanics in atmosphere and oceans, as well as the magneto-micropolar fluid system from the theory of microfluids.

Journal ArticleDOI
TL;DR: In this article, two reliable analytical methods have been devised for getting new exact analytical solutions of wick-type stochastic time-fractional Benjamin-Bona-Mahony (BBM) equatio...
Abstract: Objectives: In the paper, two new reliable analytical methods have been devised for getting new exact analytical solutions of wick-type stochastic time-fractional Benjamin-Bona-Mahony (BBM) equatio...

Journal ArticleDOI
TL;DR: In this paper, a stochastic differential equation (SDE) was derived and examined for approximately modeling the breaking down of rock surfaces through random processes, and the results showed that the SDE can be applied to a wide variety of surfaces.
Abstract: A stochastic differential equation (SDE) is derived and examined for approximately modeling the breaking down of rock surfaces through random processes. The rock surfaces include, for examp...

Journal ArticleDOI
TL;DR: In this article, nonparametric estimation of trend coefficient in models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with small noise is discussed.
Abstract: We discuss nonparametric estimation of trend coefficient in models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with small noise.