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Zbl 1190.60045
Lin, Aihong; Ren, Yong; Xia, Ningmao
On neutral impulsive stochastic integro-differential equations with infinite delays via fractional operators. (English)
[J] Math. Comput. Modelling 51, No. 5-6, 413-424 (2010). ISSN 0895-7177

Summary: We study the existence of mild solutions for a class of neutral impulsive stochastic integro-differential equations with infinite delays. We assume that the undelayed part generates an analytic resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the Sadovskii fixed point theorem combined with theories of analytic resolvent operators. An example is given to illustrate the theory.

MSC 2000:: *60H10 Stochastic ordinary differential equations
34K50 Stochastic delay equations
45R05 Random integral equations
60H20 Stochastic integral equations

Keywords: stochastic integro-differential equation; neutral equation; impulsive equation; analytic resolvent

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Zentralblatt MATH Berlin [Germany]