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arXiv · 1010.4530

Exponential mixing for some SPDEs with L\'evy noise

Enrico Priola·Jerzy Zabczyk·Lihu Xu
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Abstract

We show how gradient estimates for transition semigroups can be used to establish exponential mixing for a class of Markov processes in infinite dimensions. We concentrate on semilinear systems driven by cylindrical $\alpha$-stable noises, $\alpha \in (0,2)$, introduced in Priola-Zabczyk "Structural properties of semilinear SPDEs driven by cylindrical stable processes" (PTRF to appear). We first prove that if the nonlinearity is bounded, then the system is ergodic and strong mixing. Then we show that the system is exponentially mixing provided that the nonlinearity, or its Lipschitz constant, are sufficiently small.

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Enrico Priola, Jerzy Zabczyk, Lihu Xu. 2010-10-21. Exponential mixing for some SPDEs with L\'evy noise. https://arxiv.org/abs/1010.4530

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