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Exponential mixing of 2D SDEs forced by degenerate Lévy noises

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Abstract

We modify the coupling method established in Shirikyan (Exponential mixing for randomly forced partial differential equations: method of coupling, Springer, New York, 2008) and Shirikyan (J Math Fluid Mech 6(2):169–193, 2004) and develop a technique to prove the exponential mixing of a 2D stochastic system forced by degenerate Lévy noises. In particular, these Lévy noises include α-stable noises (0 < α < 2). Thanks to the stimulating discussion (Nersesyan in Private communication 2011), this technique is promising to study the exponential mixing problem of SPDEs driven by degenerate symmetric α-stable noises.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau

    Lihu Xu

  2. Department of Mathematics, Brunel University, Kingston Lane, Uxbridge, Middlesex, UB8 3PH, UK

    Lihu Xu

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  1. Lihu Xu
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Xu, L. Exponential mixing of 2D SDEs forced by degenerate Lévy noises. J. Evol. Equ. 14, 249–272 (2014). https://doi.org/10.1007/s00028-013-0212-4

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  • DOI: https://doi.org/10.1007/s00028-013-0212-4

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