Waveform Relaxation Methods for Stochastic Differential Equations

Waveform Relaxation Methods for Stochastic Differential Equations

Year:    2006

International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 2 : pp. 232–254

Abstract

$L^p$-convergence of waveform relaxation methods (WRMs) for numerical solving of systems of ordinary stochastic differential equations (SDEs) is studied. For this purpose, we convert the problem to an operator equation $X = \Pi X + G$ in a Banach space $\varepsilon$ of $\mathcal{F}_t$-adapted random elements describing the initial- or boundary value problem related to SDEs with weakly coupled, Lipschitz-continuous subsystems. The main convergence result of WRMs for SDEs depends on the spectral radius of a matrix associated to a decomposition of $\Pi$. A generalization to one-sided Lipschitz continuous coefficients and a discussion on the example of singularly perturbed SDEs complete this paper.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2006-IJNAM-898

International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 2 : pp. 232–254

Published online:    2006-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    waveform relaxation methods stochastic differential equations stochastic-numerical methods iteration methods large scale systems.