Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise

Details Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise

2009-09-21

arxiv.org/abs/0909.3725v1

Mathematics

Analysis of PDEs

21 pages

Scientific paper

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 $L_1$ spaces with respect to an invariant measure.

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