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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.