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

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.