Exponential mixing of 2D SDEs forced by degenerate Lévy noises

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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Correspondence to 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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Mathematics Subject Classification (2000)

  • 60H10
  • 60J75
  • 37A25

Keywords

  • SDEs driven by degenerate α-stable noises
  • coupling
  • exponential mixing