On the Markov chain central limit theorem

2004/09/07 by Galin L. Jones, Jones, Galin L. · 10 citations
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.math/0409112

openalex publication_date 2004/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• The Asymptotic Validity of Sequential Stopping Rules for Stochastic Simulations

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