Open Access
2008 A Regeneration Proof of the Central Limit Theorem for Uniformly Ergodic Markov Chains
Witold Bednorz, Krzysztof Latuszynski, Rafal Latala
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Electron. Commun. Probab. 13: 85-98 (2008). DOI: 10.1214/ECP.v13-1354


Central limit theorems for functionals of general state space Markov chains are of crucial importance in sensible implementation of Markov chain Monte Carlo algorithms as well as of vital theoretical interest. Different approaches to proving this type of results under diverse assumptions led to a large variety of CLT versions. However due to the recent development of the regeneration theory of Markov chains, many classical CLTs can be reproved using this intuitive probabilistic approach, avoiding technicalities of original proofs. In this paper we provide a characterization of CLTs for ergodic Markov chains via regeneration and then use the result to solve the open problem posed in [Roberts & Rosenthal 2005]. We then discuss the difference between one-step and multiple-step small set condition.


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Witold Bednorz. Krzysztof Latuszynski. Rafal Latala. "A Regeneration Proof of the Central Limit Theorem for Uniformly Ergodic Markov Chains." Electron. Commun. Probab. 13 85 - 98, 2008.


Accepted: 24 January 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1194.60046
MathSciNet: MR2386065
Digital Object Identifier: 10.1214/ECP.v13-1354

Primary: 60J05
Secondary: 60F05

Keywords: central limit theorems , ergodicity , Harris recurrence , Markov chains , regeneration , uniform ergodicity

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