Geodesic
Numerical solution to stochastic differential equations on supercomputers
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 5-17

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This paper deals with some issues of the dependence of the accuracy of algorithms for the numerical solutions of stochastic differential equations (SDEs) on the size of an ensemble of simulated trajectories. The problems of accuracy arise due to the necessity of estimating functionals of SDEs-solutions with an increasing dispersion, a strong asymmetry of solutions distributions, indeterminacy of the time of arrival of trajectories of solutions at the boundaries of given domains. The ways of parallelization of statistical algorithms on a multi-processor cluster are described. The results of numerical experiments obtained on the supercomputer of Siberian Supercomputer Center are presented. 
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     author = {S. S. Artemiev and V. D. Korneev},
     title = {Numerical solution to stochastic differential equations on supercomputers},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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S. S. Artemiev; V. D. Korneev. Numerical solution to stochastic differential equations on supercomputers. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 5-17. http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a1/