Stability for stochastic neutral integro-differential equations with infinite delay and Poisson jumps

Abstract

This paper investigates a kind of stochastic neutral integro-differential equations with infinite delay and Poisson jumps in the concrete-fading memory-phase space C μ . We suppose that the linear part has a resolvent operator and the nonlinear terms are globally Lipschitzian. We introduce sufficient conditions that ensure the existence and uniqueness of mild solutions by using successive approximation. Moreover, we target exponential stability, including moment exponential stability in q-th (q � 2) and almost surely exponential stability of solutions and their maps. An example illustrates the potential of the main result.