Numerical Approximation of Stationary Distributions for Stochastic Partial Differential Equations. (September 2014)

• Record Type: Journal Article
• Authors: Bao, Jianhai; Yuan, Chenggui
• Is Part Of: Journal of applied probability. Volume 51:Number 3(2014)
• Page Start: 858
• Page End: 873
• Publication Date: 2014-09
• Subjects: Stochastic partial differential equation, -- mild solution, -- stationary distribution, -- exponential integrator scheme, -- numerical approximation; 60H15, -- 65C30, -- 35K90; 519.2
• DOI: 10.1017/S0021900200011712
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : In this paper we discuss an exponential integrator scheme, based on spatial discretization and time discretization, for a class of stochastic partial differential equations. We show that the scheme has a unique stationary distribution whenever the step size is sufficiently small, and that the weak limit of the stationary distribution of the scheme as the step size tends to 0 is in fact the stationary distribution of the corresponding stochastic partial differential equations.