This article is cited in 2 papers

Numerical solution to stochastic differential equations with a random structure on supercomputers

S. S. Artemiev^ab, V. D. Korneev^a, M. A. Yakunin<sup>a

a</sup> Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent'eva 6, Novosibirsk, 630090, Russia
^b Novosibirsk State University, ul. irogova 2, Novosibirsk, 630090, Russia

Abstract: In this paper we investigate the precision of estimate of the expectation of solutions to stochastic differential equations with a random structure. The dependence of the precision of estimate on the size of the integration step of the generalized Euler method and on the volume of the simulated trajectories is shown. A strong loss of the precision of estimate at deterministic or random times of changing the SDE structure is shown on an example of a simple equation. This requires the use of supercomputers for the statistical modeling. The results of the numerical experiments carried out in the Siberian SuperСomputer Center are presented.

Key words: stochastic differential equations, parallelization, supercomputer, the methods of statistical modeling, the generalized Euler method.

UDC: 519.676

Received: 12.04.2012
Revised: 10.05.2012

 English version: Numerical Analysis and Applications, 2013, 6:4, 261–267

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