Dynamics of Partial Differential Equations
Volume 7 (2010)
Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise
Pages: 1 – 23
We study the asymptotic behavior of solutions to stochastic evolution equations with monotone drift and multiplicative Poisson noise in the variational setting, thus covering a large class of (fully) nonlinear partial differential equations perturbed by jump noise. In particular, we provide sufficient conditions for the existence, ergodicity, and uniqueness of invariant measures. Furthermore, under mild additional assumptions, we prove that the Kolmogorov equation associated to the stochastic equation with additive noise is solvable in L1 spaces with respect to an invariant measure.
stochastic PDEs, invariant measures, monotone operators, Kolmogorov equations, Poisson measures
2010 Mathematics Subject Classification
Primary 37A25, 60H15. Secondary 47H05, 60G57.