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Numerical Approximation of Stationary Distributions for Stochastic Partial Differential Equations

Part of: Stochastic analysis Parabolic equations and systems Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  30 January 2018

Jianhai Bao  and
Chenggui Yuan
Jianhai Bao*
Affiliation:
Central South University
Chenggui Yuan*
Affiliation:
Swansea University
*
∗ Postal address: Department of Mathematics, Central South University, Changsha, 410075, P. R. China. Email address: jianhaibao13@gmail.com
∗∗ Postal address: Department of Mathematics, Swansea University, Singleton Park, Swansea SA2 8PP, UK. Email address: c.yuan@swansea.ac.uk
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Abstract

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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.

Keywords

Stochastic partial differential equationmild solutionstationary distributionexponential integrator schemenumerical approximation

MSC classification

Primary: 60H15: Stochastic partial differential equations
Secondary: 65C30: Stochastic differential and integral equations 35K90: Abstract parabolic equations
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 858 - 873
Copyright
© Applied Probability Trust 

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