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

作者：Marinelli Carlo^*; Roeckner Michael

来源：Electronic Journal of Probability, 2010, 15: 1528-1555.

• Stochastic PDE
• reaction-diffusion equations
• Poisson measures
• monotone operators

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.

• 出版日期2010-10-15