Boundary-Preserving Weak Approximations of some semilinear Stochastic Partial Differential Equations

Abstract: We propose a boundary-preserving numerical scheme for the weak approximations of some scalar-valued stochastic partial differential equations (SPDEs) that only takes values in a bounded domain. We only impose regularity assumptions on the drift and diffusion coefficients locally on the domain. In particular, the drift and diffusion coefficients may be non-globally Lipschitz continuous and superlinearly growing outside the domain. The scheme consists of a finite difference discretisation in space and a Lie--Trotter splitting followed by exact simulation and exact integration in time. The scheme converges in the weak sense to the mild solution with rate 1/2 in space and 1/4 in time for globally Lipschitz continuous test functions. Numerical experiments confirm that the theoretical results are sharp and we compare the proposed scheme to existing schemes for SPDEs.

numerical analysisoptimization and control

Audience: researchers in the topic

CAM seminar

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