Open Access
2004 On the Markov chain central limit theorem
Galin L. Jones
Probab. Surveys 1: 299-320 (2004). DOI: 10.1214/154957804100000051


The goal of this expository paper is to describe conditions which guarantee a central limit theorem for functionals of general state space Markov chains. This is done with a view towards Markov chain Monte Carlo settings and hence the focus is on the connections between drift and mixing conditions and their implications. In particular, we consider three commonly cited central limit theorems and discuss their relationship to classical results for mixing processes. Several motivating examples are given which range from toy one-dimensional settings to complicated settings encountered in Markov chain Monte Carlo.


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Galin L. Jones. "On the Markov chain central limit theorem." Probab. Surveys 1 299 - 320, 2004.


Published: 2004
First available in Project Euclid: 29 December 2004

zbMATH: 1189.60129
MathSciNet: MR2068475
Digital Object Identifier: 10.1214/154957804100000051

Keywords: central limit theorem , drift condition , Markov chain , mixing condition , Monte Carlo

Rights: Copyright © 2004 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.1 • 2004
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