Electron. J. Differential Equations, Vol. 2017 (2017), No. 123, pp. 1-13.

Robustness of mean-square exponential dichotomies for linear stochastic equations

Hailong Zhu, Yongxin Jiang

We present the notion of mean-square exponential dichotomies for linear stochastic differential equations. We study the robustness of the mean-square exponential dichotomies, in the sense of the existence of a mean-square exponential dichotomy for a given linear stochastic equation persists under sufficiently small linear perturbations. As a special case, we consider mean-square exponential contractions.

Submitted July 4, 2016. Published May 5, 2017.
Math Subject Classifications: 60H10, 34D09.
Key Words: Robustness; mean-square exponential contraction; mean-square exponential dichotomy; stochastic differential equations.

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Hailong Zhu
Department of Mathematics
Shanghai Normal University
Shanghai 200234, China
email: hai-long-zhu@163.com
Yongxin Jiang
Department of Mathematics
College of Science, Hohai University
Nanjing 210098, China
email: yxinjiang@126.com

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