The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory

Nummelin, Esa; Tuominen, Pekka

doi:10.1016/0304-4149(83)90037-6

Cited by 53 publications

(88 citation statements)

References 10 publications

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“…[3]). Let r ∈ Λ, then the ergodic chain Φ n is said to be subgeometrically ergodic of order r in the fnorm, (or simply (f, r)-ergodic) if for the unique invariant distribution π of the process and ∀ i ∈ X , then lim…”

Section: P N (I ·) → π(·) As N → ∞mentioning

confidence: 99%

A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

Lekgari

2016

BMSA

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Abstract. We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and show that the finiteness of the expectation, where τ △ is the hitting time on the coupling set △ and r is a subgeometric rate function, is equivalent to a sequence of Foster-Lyapunov drift conditions which imply subgeometric convergence in the Wassertein distance. We give an example for a 'family of nested drift conditions'.

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Section: P N (I ·) → π(·) As N → ∞mentioning

confidence: 99%

A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric

Lekgari

2016

BMSA

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“…Let be a subgeometric rate function. For more on subgeometric rate functions the interested reader can consult [9]. We note that if then is also a subgeometric rate function and so is provided for some constant .…”

Section: Bulletin Of Mathematical Sciences and Applications Vol 10(8)mentioning

confidence: 99%

Maximal Coupling Procedure and Stability of Continuous-Time Markov Chains

Lekgari

2014

BMSA

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Abstract. In this study we first investigate the stability of subsampled discrete Markov chains through the use of the maximal coupling procedure. This is an extension of the available results on Markov chains and is realized through the analysis of the subsampled chain , where is an increasing sequence of random stopping times. Then the similar results are realized for the stability of countable-state Continuous-time Markov processes by employing the skeleton-chain method.

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“…Then Λ is referred to as the class of subgeometric rate functions [8]. Indeed (4) implies the equivalence of the class of functions Λ 0 with the class of functions Λ.…”

Section: Subgeometric Rate Functionmentioning

confidence: 99%