On the Markov chain central limit theorem

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.

Cited by in corpus (6)

• Limit theorems for stationary Markov processes with L2-spectral gap
• Relative fixed-width stopping rules for Markov chain Monte Carlo simulations
• Central limit theorem for triangular arrays of Non-Homogeneous Markov chains
• A practical sequential stopping rule for high-dimensional MCMC and its application to spatial-temporal Bayesian models
• MCMC Confidence Intervals and Biases
• Fixed-width output analysis for Markov chain Monte Carlo