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arXiv · 1201.4465

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

S. G. Cox·J. M. A. M. van Neerven
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Abstract

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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S. G. Cox, J. M. A. M. van Neerven. 2012-01-21. Pathwise Holder convergence of the implicit Euler scheme for semi-linear SPDEs with multiplicative noise. https://arxiv.org/abs/1201.4465

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