Journal of Applied Probability

Numerical approximation of stationary distributions for stochastic partial differential equations

Jianhai Bao and Chenggui Yuan

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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.

Article information

Source
J. Appl. Probab., Volume 51, Number 3 (2014), 858-873.

Dates
First available in Project Euclid: 5 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1409932678

Digital Object Identifier
doi:10.1239/jap/1409932678

Mathematical Reviews number (MathSciNet)
MR3256231

Zentralblatt MATH identifier
1314.60124

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 65C30: Stochastic differential and integral equations 35K90: Abstract parabolic equations

Keywords
Stochastic partial differential equation mild solution stationary distribution exponential integrator scheme numerical approximation

Citation

Bao, Jianhai; Yuan, Chenggui. Numerical approximation of stationary distributions for stochastic partial differential equations. J. Appl. Probab. 51 (2014), no. 3, 858--873. doi:10.1239/jap/1409932678. https://projecteuclid.org/euclid.jap/1409932678


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