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

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