Exponential mixing for some SPDEs with Lévy noise

Details Exponential mixing for some SPDEs with Lévy noise Exponential mixing for some SPDEs with Lévy noise

2010-10-21

arxiv.org/abs/1010.4530v1

Mathematics

Analysis of PDEs

Scientific paper

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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