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

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.