Exponential stability for some stochastic neutral partial functional integrodifferential equations with delays and Poisson jumps

In this work, we study the existence, uniqueness and exponential stability in mean square of mild solutions for some stochastic neutral partial functional integrodifferential equations with delays and Poisson jumps. Sufficient conditions for the existence and exponential stability in mean square of mild solutions are derived by means of the Banach fixed point principle. We suppose that the linear part has a resolvent operator in the sense given in Grimmer (Trans. Am. Math. Soc., 273(1):333–349, 1982). An example is provided to illustrate the results of this work.