Related papers: An efficient numerical approach for stochastic evo…
In this paper, an online multiscale model reduction method is presented for stochastic partial differential equations (SPDEs) with multiplicative noise, where the diffusion coefficient is spatially multiscale and the noise perturbation…
In this article, we have analyzed the full discretization of the Stochastic semilinear Schr\"{o}dinger equation in a bounded convex polygonal domain driven by multiplicative Wiener noise. We use the finite element method for spatial…
In this paper we study the dynamics of a fast-slow Fokker-Planck partial differential equation (PDE) viewed as the evolution equation for the density of a multiscale planar stochastic differential equation (SDE). Our key focus is on the…
Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales,…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
This work focuses on the quantitative contraction rates for McKean-Vlasov stochastic differential equations (SDEs) with multiplicative noise. Under suitable conditions on the coefficients of the SDE, this paper derives explicit quantitative…
For stochastic differential equations (SDEs) with Markovian switching, whose drift and diffusion coefficients are allowed to contain superlinear terms, the backward Euler-Maruyama (BEM) method is proposed to approximate the invariant…
We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…
We study the motion of the hypersurface $(\gamma_t)_{t\geq 0}$ evolving according to the mean curvature perturbed by $\dot{w}^Q$, the formal time derivative of the $Q$-Wiener process ${w}^Q$, in a two dimensional bounded domain. Namely, we…
We investigate the longtime behavior of stochastic partial differential equations (SPDEs) with differential operators that depend on time and the underlying probability space. In particular, we consider stochastic parabolic evolution…
A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…
In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these…
In this paper, we discuss the numerical approximation of random periodic solutions (r.p.s.) of stochastic differential equations (SDEs) with multiplicative noise. We prove the existence of the random periodic solution as the limit of the…
This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time…
Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes…
In this work, we propose a stochastic version of the Rosenzweig-MacArthur model solely driven by internal demographic noise, extending classical Lotka-Volterra-type systems focused on external noise. We give a criterion for the existence…
In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift. In particular, the drift is assumed to be $\alpha$-H\"older continuous in time and bounded…
We establish a general criterion which ensures exponential mixing of parabolic Stochastic Partial Differential Equations (SPDE) driven by a non additive noise which is white in time and smooth in space. We apply this criterion on two…
This paper formulates two 3D stochastic differential equations (SDEs) of two microbial populations in a chemostat competing over a single substrate. The two models have two distinct noise sources. One is general noise whereas the other is…