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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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: http://dx.doi.org/10.1090/S0002-9939-10-10377-3
PII: S 0002-9939(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.