079788R.pdf (379.95 kB)
Numerical approximations to the stationary solutions of stochastic differential equations
journal contribution
posted on 2014-07-23, 12:29 authored by Andrei Yevik, Huaizhong ZhaoIn 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 AnalysisVolume
49Issue
4Pages
1397 - 1416Citation
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 MathematicsVersion
- AM (Accepted Manuscript)
Publication date
2011Notes
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/10.1137/100797886ISSN
0036-1429Publisher version
Language
- en