Numerical solution of stochastic differential equations on Supercomputers

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This paper deals with some problems of accuracy of algorithms for the numerical solutions of stochastic differential equations (SDEs) versus the size of the ensemble of trajectories simulated. The problems of accuracy arise in estimating functionals of SDE solutions with increasing variance, highly asymmetric distributions, and an indefinite time of arrival of trajectories of solutions at the boundaries of given domains. Some ways of parallelization of statistical algorithms on a multiprocessor cluster are described. Results of numerical experiments performed on a supercomputer available at the Siberian Supercomputer Center are presented.