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Existence of almost periodic solutions to some functional integro-differential stochastic evolution equations. (English) Zbl 1156.60046
The aim of this paper is to prove the existence and uniqueness of quadratic mean almost periodic solution for an abstract semi-linear integro-differential equation in a real separable Hilbert space . The author follows the ideas of P. H. Bezandry and T. Diagana [Appl. Anal. 86, No. 7, 819–827 (2007; Zbl 1130.34033)] for semi-linear stochastic differential equations. As an example, the author applies the results to a stochastic partial differential equation.
MSC:
60H20Stochastic integral equations
60G05Foundations of stochastic processes