WAVEFORM RELAXATION METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS

L p -convergence of waveform relaxation methods (WRMs) for nu- merical solving of systems of ordinary stochastic difierential equations (SDEs) is studied. For this purpose, we convert the problem to an operator equation X = >>X + G in a Banach space E of Ft-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 >>. A generalization to one-sided Lipschitz continuous coe-cients and a discussion on the example of singularly perturbed SDEs complete this paper.

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