Computable Convergence Rates for Subgeometrically Ergodic Markov Chains

2005/11/10 by Randal Douc, Douc, Randal, Éric Moulines +4 · 6 citations
Mathematics · #60J10 #Computable general equilibrium #Convergence (economics) #Economics #Ergodic theory #FOS: Mathematics #Macroeconomics #Markov Chains and Monte Carlo Methods #Markov chain #Mathematics #Microeconomics #Point processes and geometric inequalities #Probability (math.PR) #Pure mathematics #Statistics #Stochastic processes and statistical mechanics #math.PR #msc:60J10

paper · pdf · open access · doi:10.48550/arxiv.math/0511273

published in arXiv (Cornell University) (Cornell University)

arxiv created 2005/11/10 · openalex publication_date 2005/11/10 · arxiv updated 2009/12/01 · 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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