Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise

Carlo Marinelli; Giacomo Ziglio

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arXiv · 0909.3725

Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise

Carlo Marinelli·Giacomo Ziglio

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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 $L_1$ spaces with respect to an invariant measure.

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Carlo Marinelli, Giacomo Ziglio. 2009-09-21. Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise. https://arxiv.org/abs/0909.3725

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