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arXiv · 1505.05061

High-order integrator for sampling the invariant distribution of a class of parabolic SPDEs with additive space-time noise

Charles-Edouard Bréhier·Gilles Vilmart
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Abstract

We introduce a time-integrator to sample with high order of accuracy the invariant distribution for a class of semilinear SPDEs driven by an additive space-time noise. Combined with a postprocessor, the new method is a modification with negligible overhead of the standard linearized implicit Euler-Maruyama method. We first provide an analysis of the integrator when applied for SDEs (finite dimension), where we prove that the method has order $2$ for the approximation of the invariant distribution, instead of $1$. We then perform a stability analysis of the integrator in the semilinear SPDE context, and we prove in a linear case that a higher order of convergence is achieved. Numerical experiments, including the semilinear heat equation driven by space-time white noise, confirm the theoretical findings and illustrate the efficiency of the approach.

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Charles-Edouard Bréhier, Gilles Vilmart. 2015-05-19. High-order integrator for sampling the invariant distribution of a class of parabolic SPDEs with additive space-time noise. https://doi.org/10.1137/15m1021088

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