Abstract
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.
Citation
Carlo Marinelli. Michael Roeckner. "Well-Posedness and Asymptotic Behavior for Stochastic Reaction-Diffusion Equations with Multiplicative Poisson Noise." Electron. J. Probab. 15 1529 - 1555, 2010. https://doi.org/10.1214/EJP.v15-818
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