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

Charles-Edouard Bréhier, Gilles Vilmart

Published 2015-05-19Version 1

We introduce an integrator to sample with high-order of accuracy the invariant distribution for a class of semilinear SPDEs driven by a additive space-time noise. Using a postprocessor, the scheme is a modification with negligible overhead of the standard linearized implicit Euler-Maruyama method. It has an improved order of convergence $r+1$, where $r$ is the order of convergence of the original method. An analysis is provided in finite dimension for nonlinear SDE problems, and in infinite dimension in a linear case. Numerical experiments, including the stochastic nonlinear heat equation with space-time noise confirm the theoretical findings and illustrate the efficiency of the approach.