Practical drift conditions for subgeometric rates of convergence

2004/07/08 by Randal Douc, Gersende Fort, Eric Moulines +1 · 2 citations
Mathematics · #Markov Chains and Monte Carlo Methods #Random Matrices and Applications #Statistical Methods and Inference #math.PR #msc:60J10.

paper · pdf · doi:10.1214/105051604000000323

published as Annals of Probability 2004, Vol. 14, No. 3, 1353-1377

arxiv created 2004/07/08 · openalex publication_date 2004/07/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a ψ-irreducible aperiodic and positive recurrent transition kernel. This condition, extending a condition introduced by Jarner and Roberts [Ann. Appl. Probab. 12 (2002) 224–247] for polynomial convergence rates, turns out to be very convenient to prove subgeometric rates of convergence. Several applications are presented including nonlinear autoregressive models, stochastic unit root models and multidimensional random walk Hastings–Metropolis algorithms.

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