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Estimate the exponential convergence rate of f-ergodicity via spectral gap

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  • Guo, Xianping
  • Liao, Zhong-Wei

Abstract

This paper studies the f-ergodicity and its exponential convergence rate for continuous-time Markov chain. Assume f is square integrable, for reversible Markov chain, it is proved that the exponential convergence of f-ergodicity holds if and only if the spectral gap of the generator is positive. Moreover, the convergence rate is equal to the spectral gap. For irreversible case, the positivity of spectral gap remains a sufficient condition of f-ergodicity. The effectiveness of these results are illustrated by some typical examples.

Suggested Citation

  • Guo, Xianping & Liao, Zhong-Wei, 2021. "Estimate the exponential convergence rate of f-ergodicity via spectral gap," Statistics & Probability Letters, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:stapro:v:168:y:2021:i:c:s0167715220302273
    DOI: 10.1016/j.spl.2020.108924
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    References listed on IDEAS

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    1. Chen, Mu-Fa, 2000. "Equivalence of exponential ergodicity and L2-exponential convergence for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 281-297, June.
    2. Douc, Randal & Fort, Gersende & Guillin, Arnaud, 2009. "Subgeometric rates of convergence of f-ergodic strong Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 897-923, March.
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