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. 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.

Exponential mixing for some SPDEs with Levy noise

PRIOLA, Enrico;
2011-01-01

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. 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.
2011
11
521
534
http://arxiv.org/pdf/1010.4530v1
http://www.worldscinet.com/sd/11/1102n03/S0219493711003425.html
Exponential mixing
E. Priola; L. Xu; J. Zabczyk
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/90555
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