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Title: Numerical approximations to the stationary solutions of stochastic differential equations
Authors: Yevik, Andrei
Zhao, Huaizhong
Keywords: Random dynamical system
Stationary solution
Numerical approximation
Issue Date: 2011
Publisher: © Society for Industrial and Applied Mathematics
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.
Abstract: 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.
Description: 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
Version: Accepted for publication
DOI: 10.1137/100797886
URI: https://dspace.lboro.ac.uk/2134/15310
Publisher Link: http://dx.doi.org/10.1137/100797886
ISSN: 0036-1429
Appears in Collections:Published Articles (Maths)

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