Well posedness and asymptotic behavior for stochastic reaction-diffusion equations with multiplicative Poisson noise
Carlo Marinelli, University of Bolzano
Michael Roeckner, University of Bielefeld
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
Lp spaces.
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