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Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2016

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

Résumé

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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Dates et versions

hal-01153448 , version 1 (19-05-2015)
hal-01153448 , version 2 (01-06-2016)

Identifiants

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Charles-Edouard Bréhier, Gilles Vilmart. High Order Integrator for Sampling the Invariant Distribution of a Class of Parabolic Stochastic PDEs with Additive Space-Time Noise. SIAM Journal on Scientific Computing, 2016, 38 (4), ⟨10.1137/15M1021088⟩. ⟨hal-01153448v2⟩
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