Spatial approximation of stochastic convolutions. (English) Zbl 1229.65027
This paper studies the behaviour of a linear stochastic evolution problem with additive noise. The authors present a general framework for representing the infinite-dimensional Wiener process and obtain error estimates for truncated expansions which they then combine with a finite element analysis to obtain bounds for the mean square error.
Reviewer: Kevin Burrage (Brisbane)
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65T60 | Numerical methods for wavelets |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
Keywords:
finite element; wavelet; stochastic heat equation; stochastic wave equation; Wiener process; additive noiseReferences:
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