@Article{IJNAM-3-232,
author = {H. Schurz and K. R. Schneider},
title = {Waveform Relaxation Methods for Stochastic Differential Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2006},
volume = {3},
number = {2},
pages = {232--254},
abstract = {<p style="text-align: justify;">$L^p$-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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/898.html}
}