Well-posedness for a class of dissipative stochastic evolution equations with Wiener and Poisson noise

TL;DR

This paper establishes existence and uniqueness of solutions for a class of stochastic evolution equations driven by Wiener and Poisson noise, extending previous results to include jump-diffusion cases.

Contribution

It extends prior work by proving well-posedness for stochastic equations with both Wiener and Poisson noise, incorporating polynomial growth conditions.

Findings

Proves existence of mild solutions

Establishes uniqueness of solutions

Extends results to jump-diffusion noise cases

Abstract

We prove existence and uniqueness of mild and generalized solutions for a class of stochastic semilinear evolution equations driven by additive Wiener and Poisson noise. The non-linear drift term is supposed to be the evaluation operator associated to a continuous monotone function satisfying a polynomial growth condition. The results are extensions to the jump-diffusion case of the corresponding ones proved in [4] for equations driven by purely discontinuous noise.