Numerical analysis of semilinear stochastic evolution equations in Banach spaces
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 stoc...
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Published in | Journal of computational and applied mathematics Vol. 147; no. 2; pp. 485 - 516 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Amsterdam
Elsevier B.V
15.10.2002
Elsevier |
Subjects | |
Online Access | Get full text |
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Summary: | 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
L
p
-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. |
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ISSN: | 0377-0427 1879-1778 |
DOI: | 10.1016/S0377-0427(02)00483-1 |