In this paper, we investigate the existence of mild solutions for a class of stochastic functional differential impulsive equations with infinite delay on Hilbert space. The results are obtained by using the Banach fixed point theorem and Krasnoselskii-Schaefer type fixed point theorem combined with theories of resolvent operators. In the end as an application, an example has been presented to illustrate the results obtained.

This paper presents conditions to assure existence, uniqueness and stability for impulsive neutral stochastic integrodifferential equations with delay driven by Rosenblatt process and Poisson jumps. The Banach fixed point theorem and the theory of resolvent operator developed by Grimmer [R.C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Am. Math. Soc., 273(1):333–349, 1982] are used. An example illustrates the potential benefits of these results.

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