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.
Almost Periodic Solutions for a Class of Stochastic Differential Equations
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.
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Liu, Y., and Liu, A. (March 26, 2013). "Almost Periodic Solutions for a Class of Stochastic Differential Equations." ASME. J. Comput. Nonlinear Dynam. October 2013; 8(4): 041002. https://doi.org/10.1115/1.4023914
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