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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:

60H20 Stochastic integral equations
60G05 Foundations of stochastic processes

Citations:

Zbl 1130.34033
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References:

[1] Bezandry, P.; Diagana, T., Existence of almost periodic solutions to some stochastic differential equations, Appl. Anal., 2007, 117, 1-10 (2007) · Zbl 1138.60323
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[4] Kannan, D.; Bharucha-Reid, D., On a Stochastic integro-differential evolution of volterra type, J. Integral Equations, 10, 351-379 (1985) · Zbl 0583.60060
[5] Keck, D.; McKibben, M., Functional Integro-differential Stochastic evolution equations in Hilbert space, J. Appl. Math. Stoch. Anal., 16, 2, 141-161 (2003) · Zbl 1031.60061
[6] Keck, D.; McKibben, M., Abstract Stochastic integro-differential delay equations, J. Appl. Math. Stoch. Anal., 3, 275-305 (2005) · Zbl 1105.60045
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