Computable Convergence Rates for Subgeometrically Ergodic Markov Chains

2005/11/10 by Randal Douc, Éric Moulines, Douc, Randal +3
Mathematics · #60J10 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.math/0511273

openalex publication_date 2005/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give quantitative bounds on the f-total variation distance from convergence of an Harris recurrent Markov chain on an arbitrary under drift and minorisation conditions implying ergodicity at a sub-geometric rate. These bounds are then specialized to the stochastically monotone case, covering the case where there is no minimal reachable element. The results are illustrated on two examples from queueing theory and Markov Chain Monte Carlo.

Citations

• Renewal theory and computable convergence rates for geometrically ergodic Markov chains

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