Central limit theorem started at a point for additive functionals of reversible Markov chains

2009/10/14 by Christophe Cuny, Cuny, Christophe, Magda Peligrad +1
Mathematics · #60F05 #60F15 #60J05 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0910.2631

openalex publication_date 2009/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the almost sure central limit theorem started from a point for additive functionals of a stationary and ergodic Markov chain via a martingale approximation in the almost sure sense. As a consequence we derive the quenched CLT for additive functionals or reversible Markov chains.

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