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Criteria for ergodicity of Lévy type operators in dimension one

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  • Wang, Jian

Abstract

Some sufficient conditions for the recurrence, the positive recurrence and the exponential ergodicity of one-dimensional Lévy type operators are presented. The conditions are classified according to different conditions on the ranges and integrability of the Lévy measure, based on the drift inequalities for the extended generator, and on a comparison with diffusion operators. A number of examples are illustrated, including the fractional Laplacian operator and the Ornstein-Uhlenbeck type operator.

Suggested Citation

  • Wang, Jian, 2008. "Criteria for ergodicity of Lévy type operators in dimension one," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1909-1928, October.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:10:p:1909-1928
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    Cited by:

    1. Song, Yan-Hong, 2016. "Algebraic ergodicity for SDEs driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 108-115.
    2. Sandrić, Nikola, 2013. "Long-time behavior of stable-like processes," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1276-1300.
    3. Wang, Tao, 2022. "Ergodic convergence rates for time-changed symmetric Lévy processes in dimension one," Statistics & Probability Letters, Elsevier, vol. 183(C).
    4. Wang, Jian, 2010. "Regularity of semigroups generated by Lévy type operators via coupling," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1680-1700, August.

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