Marinelli, Carlo; Roeckner, Michael Well posedness and asymptotic behavior for stochastic reaction-diffusion equations with multiplicative Poisson noise. (English) Zbl 1225.60108 Electron. J. Probab. 15, Paper No. 48, 1529-1555 (2010). Summary: 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 the 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. Cited in 1 ReviewCited in 20 Documents MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60G57 Random measures Keywords:stochastic PDE; reaction-diffusion equations; Poisson measures; monotone operators PDFBibTeX XMLCite \textit{C. Marinelli} and \textit{M. Roeckner}, Electron. J. Probab. 15, Paper No. 48, 1529--1555 (2010; Zbl 1225.60108) Full Text: DOI arXiv EMIS