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Ergodic convergence rates for time-changed symmetric Lévy processes in dimension one

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  • Wang, Tao

Abstract

We obtain the lower bounds for ergodic convergence rates, including spectral gap and convergence rate in strong ergodicity for time-changed symmetric Lévy processes by using harmonic function and reversible measure. As direct applications, explicit sufficient conditions for exponential and strong ergodicity are given. Some examples are also presented.

Suggested Citation

  • Wang, Tao, 2022. "Ergodic convergence rates for time-changed symmetric Lévy processes in dimension one," Statistics & Probability Letters, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:stapro:v:183:y:2022:i:c:s0167715221002893
    DOI: 10.1016/j.spl.2021.109343
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    References listed on IDEAS

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    1. Chen, Zhen-Qing & Wang, Jian, 2014. "Ergodicity for time-changed symmetric stable processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2799-2823.
    2. 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.
    3. Luo, Dejun & Wang, Jian, 2019. "Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3129-3173.
    4. Mao, Yong-Hua, 2006. "Convergence rates in strong ergodicity for Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1964-1976, December.
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