Well-posedness and asymptotic behavior for stochastic reaction-diffusion equations with multiplicative Poisson noise

Marinelli C, Röckner M. Well-posedness and asymptotic behavior for stochastic reaction-diffusion equations with multiplicative Poisson noise. Electronic Journal of Probability . 2010;15:1528-1555.We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of invariant measures for the associated semigroup in the Markovian case. A key role is played by a new maximal inequality for stochastic convolutions in L-p spaces