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On the local limit theorem for non-uniformly ergodic Markov chains

Part of: Limit theorems

Published online by Cambridge University Press:  14 July 2016

Marc Séva
Marc Séva*
Affiliation:
Université de Bretagne Occidentale
*
∗Postal address: Département de Mathématiques, Université de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu BP 452, 29275 Brest Cedex, France.
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Abstract

Using an approach similar to that of Guivarc'h and Hardy (1988), we show that the local limit theorem holds for a Markov chain on a countable state space, with non-uniform ergodicity, when the recurrence is fast enough. We present a detailed study of a typical example, the reflected random walk on the positive half-line with negative mean and finite exponential moment. The results can be extended to some random walks on ℕ.

Keywords

CENTRAL LIMIT THEOREMRANDOM WALKPERTURBATION METHODS

MSC classification

Secondary: 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 52 - 62
Copyright
Copyright © Applied Probability Trust 1995 

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