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Title

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

Authors
Bréhier, Charles-Edouard
Published in SIAM Journal on Scientific Computing. 2016, vol. 38, no. 4, p. A2283-A2306
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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Research group Analyse numérique
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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. https://archive-ouverte.unige.ch/unige:86147

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Deposited on : 2016-08-17

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