, Volume 30, Issue 5, pp 881-898
Date: 24 Aug 2013

Square-mean almost periodic solutions to some stochastic evolution equations

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Abstract

This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called “Acquistapace-Terreni” conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.

Supported by National Natural Science Foundation of China (Grant Nos. 11201266 and 11171191), Tianyuan Youth Foundation of National Natural Science Foundation of China (Grant Nos. 11026150 and 11026098) and Excellent Youth Foundation of Shandong Institute of Business and Technology