Numerical stationary distribution and its convergence for nonlinear stochastic differential equations

Wei Liu; Xuerong Mao

doi:10.1016/j.cam.2014.08.019

Numerical stationary distribution and its convergence for nonlinear stochastic differential equations

Wei Liu, Xuerong Mao

Mathematics And Statistics

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Abstract

To avoid finding the stationary distributions of stochastic differential equations by solving the nontrivial Kolmogorov-Fokker-Planck equations, the numerical stationary distributions are used as the approximations instead. This paper is devoted to approximate the stationary distribution of the underlying equation by the Backward Euler-Maruyama method. Currently existing results [21, 31, 33] are extended in this paper to cover larger range of nonlinear SDEs when the linear growth condition on the drift coeffcient is violated.

Original language	English
Pages (from-to)	16-29
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	276
Early online date	27 Aug 2014
DOIs	https://doi.org/10.1016/j.cam.2014.08.019
Publication status	Published - 1 Mar 2015

Keywords

the backward Euler-Maruyama method
weak convergence
numerical stationary distribution
nonlinear SDEs

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Numerical stationary distribution and its convergence for nonlinear stochastic differential equationsAccepted author manuscript, 339 KB

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abstract = "To avoid finding the stationary distributions of stochastic differential equations by solving the nontrivial Kolmogorov-Fokker-Planck equations, the numerical stationary distributions are used as the approximations instead. This paper is devoted to approximate the stationary distribution of the underlying equation by the Backward Euler-Maruyama method. Currently existing results [21, 31, 33] are extended in this paper to cover larger range of nonlinear SDEs when the linear growth condition on the drift coeffcient is violated.",

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AB - To avoid finding the stationary distributions of stochastic differential equations by solving the nontrivial Kolmogorov-Fokker-Planck equations, the numerical stationary distributions are used as the approximations instead. This paper is devoted to approximate the stationary distribution of the underlying equation by the Backward Euler-Maruyama method. Currently existing results [21, 31, 33] are extended in this paper to cover larger range of nonlinear SDEs when the linear growth condition on the drift coeffcient is violated.

KW - the backward Euler-Maruyama method

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KW - numerical stationary distribution

KW - nonlinear SDEs

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

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Numerical stationary distribution and its convergence for nonlinear stochastic differential equations

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