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Research Papers

Almost Periodic Solutions for a Class of Stochastic Differential Equations

[+] Author and Article Information
Yongjian Liu

School of Mathematics and Information Science,
Yulin Normal University,
Yulin 537000, PRC
e-mail: liuyongjianmaths@126.com

Aimin Liu

Department of Experiment and Equipment,
Yulin Normal University,
Yulin 537000, PRC
e-mail: aiminliumaths@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received October 16, 2011; final manuscript received September 6, 2012; published online March 26, 2013. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 8(4), 041002 (Mar 26, 2013) (6 pages) Paper No: CND-11-1175; doi: 10.1115/1.4023914 History: Received October 16, 2011; Revised September 06, 2012

In this paper, the existence and uniqueness of the square-mean almost periodic solutions to a class of the semilinear stochastic equations is studied. In particular, the condition of the uniform exponential stability of the linear operator is essentially removed, only using the exponential dichotomy of the linear operator. Some new criteria ensuring the existence and uniqueness of the square-mean almost periodic solution for the system are presented. Finally, an example of a kind of the stochastic cellular neural networks is given. These obtained results are important in signal processing and the in design of networks.

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Figures

Grahic Jump Location
Fig. 1

Behavior of the stochastic system (12)

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