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$L^p$-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.
}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/898.html} }$L^p$-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.