Pathwise Holder convergence of the implicit Euler scheme for semi-linear SPDEs with multiplicative noise

Details Pathwise Holder convergence of the implicit Euler scheme for semi-linear SPDEs with multiplicative noise Pathwise Holder convergence of the implicit Euler scheme for semi-linear SPDEs with multiplicative noise

2012-01-21

arxiv.org/abs/1201.4465v1

Mathematics

Functional Analysis

67 pages

Scientific paper

In this article we prove pathwise Holder convergence with optimal rates of the implicit Euler scheme for semi-linear parabolic stochastic differential equations with multiplicative noise, set in a UMD Banach space X. We assume the non-linearities to satisfy appropriate (local) Lipschitz conditions. The convergence results are obtained by first proving corresponding results for the splitting scheme. The results are applied to a class of second order parabolic SPDEs driven by multiplicative space-time white noise.

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