A martingale proof of Dobrushin's theorem for non-homogeneous Markov chains

2004/04/12 by Sunder Sethuraman, Sethuraman, Sunder, S. R. S. Varadhan +1 · 5 citations
Mathematics · #60F05 (secondary) #60J10 (primary) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60F05 #msc:60J10

paper · pdf · doi:10.48550/arxiv.math/0404231

15 pages

arxiv created 2004/04/12 · openalex publication_date 2004/04/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1956, Dobrushin proved a definitive central limit theorem for non-homogeneous Markov chains. In this note, a shorter and different proof elucidating more the assumptions is given through martingale approximation.

Cited by

• Limit theorems for inhomogeneous random walks on GL(d,\mathbb R)
• Statistical properties of Markov shifts: part II-LLT
• Limit theorems for inhomogeneous ϕ-mixing Markov chains
• Statistical properties of Markov shifts (part I)
• On conditions for Dobrushin's Central limit theorem for non-homogeneous Markov chains

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