Well-posedness for a class of dissipative stochastic evolution equations   with Wiener and Poisson noise
  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. 
Carlo Marinelli
math.AP math.PR