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Asymptotic behavior of neutral stochastic partial functional integro-differential equations driven by a fractional Brownian motion. (English) Zbl 1322.60103
Summary: This paper deals with the existence, uniqueness and asymptotic behavior of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion \(B^H\) with Hurst parameter \(H \in (\frac12, 1)\). The main tools for the existence of a solution is a fixed point theorem and the theory of resolvent operators developed in [R. C. Grimmer, Trans. Am. Math. Soc. 273, 333–349 (1982; Zbl 0493.45015)], while a Gronwall-type lemma plays the key role for the asymptotic behavior. An example is provided to illustrate the results of this work.

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
60G22 Fractional processes, including fractional Brownian motion
60G15 Gaussian processes
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