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The purpose of this paper is to study stochastic evolution inclusions of theform \begin{align*}  \eta(t,z) N_{\Theta}(dt \otimes z)\in dX(t)+\mathcal{A} X(t)dt, \end{align*}where $\mathcal{A}$ is a multi-valued operator acting on a separable Banachspace and $N_{\Theta}$ is the counting measure induced by a point process$\Theta$. Firstly, we will set up the concepts of strong and mild solutions;then we will derive existence as well as uniqueness criteria for these kinds ofsolutions and give a representation formula for the solutions. The results willbe formulated by means of nonlinear semigroup theory and except forseparability, no assumptions on the underlying Banach space are required.

Abstract Cauchy Problems in separable Banach Spaces driven by random Measures: Existence and Uniqueness