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

S. G. Cox; J. M. A. M. van Neerven

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

Functional Analysis 2012-01-24 v1 Numerical Analysis Probability

Authors: S. G. Cox , J. M. A. M. van Neerven

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.

Keywords

stochastic differential equations stochastic partial differential equations partial differential equations

Cite

@article{arxiv.1201.4465,
  title  = {Pathwise Holder convergence of the implicit Euler scheme for semi-linear SPDEs with multiplicative noise},
  author = {S. G. Cox and J. M. A. M. van Neerven},
  journal= {arXiv preprint arXiv:1201.4465},
  year   = {2012}
}

Comments

67 pages

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