Related papers: Stochastic functional partial differential equatio…
The main goal of this article is to study the effect of small, highly nonlinear, unbounded drifts (small time large deviation principle (LDP) based on exponential equivalence arguments) for a class of stochastic partial differential…
This paper studies the stability properties of stochastic differential equations subject to persistent noise (including the case of additive noise), which is noise that is present even at the equilibria of the underlying differential…
We prove new concentration estimates for random variables that are functionals of a Poisson measure defined on a general measure space. Our results are specifically adapted to geometric applications, and are based on a pervasive use of a…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
In this paper, we first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the…
In this paper, we aim to study the asymptotic behaviour for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational approach and classical Khasminskii time discretization, we…
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…
We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…
This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random measure, more realistic in modeling real world phenomena.…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
In this paper, we study the existence, stability and bifurcation of random complete and periodic solutions for stochastic parabolic equations with multiplicative noise. We first prove the existence and uniqueness of tempered random…
In this paper we establish the strong existence, pathwise uniqueness and a comparison theorem to a stochastic partial differential equation driven by Gaussian colored noise with non-Lipschitz drift, H\"older continuous diffusion…
We study a compound Poisson (random time-change) approximation for stochastic differential equations (SDEs) and stochastic Volterra equations whose coefficients may be merely measurable in time and may even exhibit integrable singularities.…
In this work we study the long time behavior of nonlinear stochastic functional-differential equations in Hilbert spaces. In particular, we start with establishing the existence and uniqueness of mild solutions. We proceed with deriving a…
We consider a stochastic partial differential equation (SPDE) model for chemorepulsion, with non-linear sensitivity on the one-dimensional torus. We show that for any suitable initial data there exists a pathwise unique, global solution to…
We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…
The paper is dedicated to studying the problem of existence and uniqueness of solutions as well as existence of and exponential convergence to invariant measures for McKean-Vlasov stochastic differential equations with Markovian switching.…
The existence and uniqueness of the numerical invariant measure of the backward Euler-Maruyama method for stochastic differential equations with Markovian switching is yielded, and it is revealed that the numerical invariant measure…
In this paper, a general theorem on the equivalence of pth moment stability between stochastic differential delay equations (SDDEs) and their numerical methods is proved under the assumptions that the numerical methods are strongly…