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High Order Integrator for Sampling the Invariant Distribution of a Class of Parabolic Stochastic PDEs with Additive Space-Time Noise

Published inSIAM journal on scientific computing, vol. 38, no. 4, p. A2283-A2306
Publication date2016
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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Citation (ISO format)
BRÉHIER, Charles-Edouard, VILMART, Gilles. High Order Integrator for Sampling the Invariant Distribution of a Class of Parabolic Stochastic PDEs with Additive Space-Time Noise. In: SIAM journal on scientific computing, 2016, vol. 38, n° 4, p. A2283–A2306. doi: 10.1137/15M1021088
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ISSN of the journal1064-8275
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Creation08/16/2016 10:45:00 PM
First validation08/16/2016 10:45:00 PM
Update time03/15/2023 12:38:06 AM
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