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Numerical approximations to the stationary solutions of stochastic differential equations

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journal contribution
posted on 2014-07-23, 12:29 authored by Andrei Yevik, Huaizhong Zhao
In this paper, we investigate the possibility of approximating the stationary solution of a stochastic differential equation (SDE). We start with the random dynamical system generated by the SDE with the multiplicative noise. We prove that the pullback flow has a stationary point. However, the stationary point is not constructible explicitly; therefore, we look at the numerical approximation. We prove that the discrete time random dynamical system also has a stationary point. Finally, we prove mean-square convergence of the approximate stationary solution to the exact stationary solution as the time step diminishes, as well as almost surely convergence when the time step is rational.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

SIAM Journal on Numerical Analysis

Volume

49

Issue

4

Pages

1397 - 1416

Citation

YEVIK, A. and ZHAO, H., 2011. Numerical approximations to the stationary solutions of stochastic differential equations. SIAM Journal on Numerical Analysis, 49 (4), pp. 1397 - 1416.

Publisher

© Society for Industrial and Applied Mathematics

Version

  • AM (Accepted Manuscript)

Publication date

2011

Notes

This article was published in the journal, SIAM Journal on Numerical Analysis [© Society for Industrial and Applied Mathematics] and the definitive version is available at: http://dx.doi.org/10.1137/100797886

ISSN

0036-1429

Language

  • en

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