Numerical Approximation of Stationary Distributions for Stochastic Partial Differential Equations. (30th January 2018) - Bao, Jianhai; Yuan, Chenggui
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.