Square-mean almost automorphic solutions for some stochastic differential equations

Authors:
Miaomiao Fu and Zhenxin Liu

Journal:
Proc. Amer. Math. Soc. **138** (2010), 3689-3701

MSC (2010):
Primary 60H25, 34C27, 34F05, 34G20

Published electronically:
May 6, 2010

MathSciNet review:
2661567

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Abstract | References | Similar Articles | Additional Information

Abstract: The concept of square-mean almost automorphy for stochastic processes is introduced. The existence and uniqueness of square-mean almost automorphic solutions to some linear and non-linear stochastic differential equations are established provided the coefficients satisfy some conditions. The asymptotic stability of the unique square-mean almost automorphic solution in the square-mean sense is discussed.

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Additional Information

**Miaomiao Fu**

Affiliation:
College of Mathematics, Jilin University, Changchun 130012, People’s Republic of China – and – School of Mathematics, Changchun Normal College, Changchun 130032, People’s Republic of China

Email:
mmfucaathy@yahoo.com.cn

**Zhenxin Liu**

Affiliation:
College of Mathematics, Jilin University, Changchun 130012, People’s Republic of China

Email:
zxliu@jlu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-10-10377-3

Keywords:
Almost automorphy,
stochastic differential equations

Received by editor(s):
October 27, 2009

Received by editor(s) in revised form:
January 11, 2010

Published electronically:
May 6, 2010

Additional Notes:
The second author is partially supported by NSFC Grant 10801059, SRFDP Grant 20070183053, the 985 Program of Jilin University, and the science research fund at Jilin University.

Communicated by:
Yingfei Yi

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.