Illinois Journal of Mathematics

Exponential mixing for SPDEs driven by highly degenerate Lévy noises

Xiaobin Sun, Yingchao Xie, and Lihu Xu

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By modifying a coupling method developed by the third author with much more delicate analysis, we prove that a family of stochastic partial differential equations (SPDEs) driven by highly degenerate pure jump Lévy noises are exponential mixing. These pure jump Lévy noises include a finite dimensional α-stable process with α(0,2).

Article information

Illinois J. Math., Volume 63, Number 1 (2019), 75-102.

Received: 26 April 2018
Revised: 1 February 2019
First available in Project Euclid: 29 May 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx} 60J75: Jump processes 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]


Sun, Xiaobin; Xie, Yingchao; Xu, Lihu. Exponential mixing for SPDEs driven by highly degenerate Lévy noises. Illinois J. Math. 63 (2019), no. 1, 75--102. doi:10.1215/00192082-7600360.

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