Mean-square almost automorphic solutions for stochastic differential equations with hyperbolicity

Hailong Zhu; Jifeng Chu; Weinian Zhang

doi:10.3934/dcds.2018078

Article Contents

2018, Volume 38, Issue 4: 1935-1953. Doi: 10.3934/dcds.2018078

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Next Article The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos

Mean-square almost automorphic solutions for stochastic differential equations with hyperbolicity

1.
School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China
2.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
3.
College of Mathematics, Sichuan University, Chengdu, China

* Corresponding author
* Corresponding author

Received: November 2016

Revised: November 2017

Published: July 2018

Jifeng Chu was supported by the National Natural Science Foundation of China (Grant No. 11671118). Hailong Zhu was supported by the National NSF of China (NO. 11301001), China Postdoctoral Science Foundation funded project (NO. 2016M591697), NSF of Anhui Province of China(NO. KJ2017A432, NO. 1708085MA17).

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Abstract

In the setting of mean-square exponential dichotomies, we study the existence and uniqueness of mean-square almost automorphic solutions of non-autonomous linear and nonlinear stochastic differential equations.

Keywords:

Mean-square almost automorphic solutions,
mean-square exponential dichotomy,
stochastic differential equations.

Mathematics Subject Classification: Primary: 60H10, 34C27, 34D09.

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