Dynamics of Partial Differential Equations

Volume 7 (2010)

Number 1

Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise

Pages: 1 – 23

DOI: https://dx.doi.org/10.4310/DPDE.2010.v7.n1.a1

Authors

Carlo Marinelli (Facoltà di Economia, Università di Bolzano, Italy)

Giacomo Ziglio (Dipartimento di Matematica, Università di Trento, Italy)

Abstract

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.

Keywords

stochastic PDEs, invariant measures, monotone operators, Kolmogorov equations, Poisson measures

2010 Mathematics Subject Classification

Primary 37A25, 60H15. Secondary 47H05, 60G57.

Published 1 January 2010