Central limit theorem for triangular arrays of Non-Homogeneous Markov chains

2010/12/29 by Magda Peligrad, Peligrad, Magda · 7 citations
Computer Science · Mathematics · #60F05 #60G48 #60J10 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1012.6000

openalex publication_date 2010/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower bound estimate for the variance of partial sums. The results complement an important central limit theorem of Dobrushin based on the contraction coefficient.

Citations

• On the Markov chain central limit theorem

Cited by

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• Statistical properties of Markov shifts: part II-LLT
• A simple lemma concerning the Doeblin minorization condition and its applications to limit theorems for inhomogeneous Markov chains
• Statistical properties of Markov shifts (part I)
• Predictive inference for discrete-valued time series
• On conditions for Dobrushin's Central limit theorem for non-homogeneous Markov chains

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