相关论文: Large deviations principles of sample paths and in…

In this paper, we focus on two kinds of large deviations principles (LDPs) of the invariant measures of Langevin equations and their numerical methods, as the noise intensity $\epsilon\to 0$ and the dissipation intensity $\nu\to\infty$…

This paper aims to investigate the asymptotic error distribution of several numerical methods for stochastic partial differential equations (SPDEs) with multiplicative noise. Firstly, we give the limit distribution of the normalized error…

In this paper, we consider the large deviations principles (LDPs) for the stochastic linear Schr\"odinger equation and its symplectic discretizations. These numerical discretizations are the spatial semi-discretization based on spectral…

We discrete the ergodic semilinear stochastic partial differential equations in space dimension $d \leq 3$ with additive noise, spatially by a spectral Galerkin method and temporally by an exponential Euler scheme. It is shown that both the…

Approximating the invariant measure and the expectation of the functionals for parabolic stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients is an active research area and is far from being well…

We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. We analyze the strong error of convergence for spatially…

This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial differential equations (SPDEs) with locally monotone coefficients in generalized variational framework. The main result could be…

Consider stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple $V\subseteq H\subseteq V^*$ $$ \left\{ \begin{align} &dX_t=A(t,X_t)dt+B(t,X_t)dW_t,\ t\in (0,T]\\\\& X_0=x\in H,…

In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By…

We establish the well-posedness of stationary solutions for a class of SPDEs with locally monotone coefficients, and prove the Freidlin--Wentzell large deviation principle (LDP) for these stationary solutions. The LDP for the associated…

This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function…

We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then establish the LDP for the invariant measures…

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…

We investigate the large deviation principle (LDP) of the stationary solutions of stochastic functional differential equations (SFDEs) with infinite delay under small random perturbation. First, we demonstrate the existence and uniqueness…

It is well known that symplectic methods have been rigorously shown to be superior to non-symplectic ones especially in long-time computation, when applied to deterministic Hamiltonian systems. In this paper, we attempt to study the…

This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler…

In order to inherit numerically the ergodicity of the damped stochastic nonlinear Schr\"odinger equation with additive noise, we propose a fully discrete scheme, whose spatial direction is based on spectral Galerkin method and temporal…

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.…

This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…

Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…