Existence, Uniqueness and Stability of Mild Solutions for Time-Dependent Stochastic Evolution Equations with Poisson Jumps and Infinite Delay

Abstract

In this paper, we study a class of time-dependent stochastic evolution equations with Poisson jumps and infinite delay. We establish the existence, uniqueness and stability of mild solutions for these equations under non-Lipschitz condition with Lipschitz condition being considered as a special case. An application to the stochastic nonlinear wave equation, with Poisson jumps and infinite delay, is given to illustrate the obtained theory.