Numerical analysis of semilinear stochastic evolution equations in Banach spaces

Authors:
Erika Hausenblas
Affiliations:
University Salzburg, Department of Mathematics, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Abstract

The solution of stochastic evolution equations generally relies on numerical computation. Here, usually the main idea is to discretize the SPDE spatially obtaining a system of SDEs that can be solved by e.g., the Euler scheme. In this paper, we investigate the discretization error of semilinear stochastic evolution equations in Lp-spaces, resp. Banach spaces. The space discretization may be done by Galerkin approximation, for the time discretization we consider the implicit Euler, the explicit Euler scheme and the Crank-Nicholson scheme. In the last section, we give some examples i.e., we consider an SPDEs driven by nuclear Wiener noise approximated by wavelets and delay equation approximated by finite differences.