Square-mean almost periodic solutions to some stochastic evolution equations
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- Li, X.L. Acta. Math. Sin.-English Ser. (2014) 30: 881. doi:10.1007/s10114-013-1109-4
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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.