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We establish well-posedness in the mild sense for a class of stochasticsemilinear evolution equations with a polynomially growing quasi-monotonenonlinearity and multiplicative Poisson noise. We also study existence anduniqueness of invariant measures for the associated semigroup in the Markoviancase. A key role is played by a new maximal inequality for stochasticconvolutions in $L_p$ spaces.

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