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State-dependent Foster-Lyapunov criteria for subgeometric convergence of Markov chains

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  • Connor, S.B.
  • Fort, G.

Abstract

We consider a form of state-dependent drift condition for a general Markov chain, whereby the chain subsampled at some deterministic time satisfies a geometric Foster-Lyapunov condition. We present sufficient criteria for such a drift condition to exist, and use these to partially answer a question posed in Connor and Kendall (2007) [2] concerning the existence of so-called 'tame' Markov chains. Furthermore, we show that our 'subsampled drift condition' implies the existence of finite moments for the return time to a small set.

Suggested Citation

  • Connor, S.B. & Fort, G., 2009. "State-dependent Foster-Lyapunov criteria for subgeometric convergence of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4176-4193, December.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:12:p:4176-4193
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    References listed on IDEAS

    as
    1. Fort, G. & Moulines, E., 2003. "Polynomial ergodicity of Markov transition kernels," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 57-99, January.
    2. Nummelin, Esa & Tuominen, Pekka, 1983. "The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 295-311, August.
    3. 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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