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Asymptotic stability of neutral stochastic functional integro-differential equations with impulses. (English) Zbl 1308.93212
Summary: This paper is concerned with the existence and asymptotic stability in the \(p\)-th moment of mild solutions of nonlinear impulsive stochastic delay neutral partial functional integro-differential equations. We suppose that the linear part possesses a resolvent operator in the sense given by Grimmer and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is used to achieve the required result. An example is provided to illustrate the theory developed in this work.

MSC:
93E15 Stochastic stability in control theory
34K50 Stochastic functional-differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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