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

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

2009-03-19

arxiv.org/abs/0903.3299v3

Mathematics

Probability

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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.

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