The Annals of Applied Probability

Practical drift conditions for subgeometric rates of convergence

Randal Douc, Gersende Fort, Eric Moulines, and Philippe Soulier

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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.

Article information

Source
Ann. Appl. Probab., Volume 14, Number 3 (2004), 1353-1377.

Dates
First available in Project Euclid: 13 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1089736288

Digital Object Identifier
doi:10.1214/105051604000000323

Mathematical Reviews number (MathSciNet)
MR2071426

Zentralblatt MATH identifier
1082.60062

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Markov chains stationary distribution rate of convergence

Citation

Douc, Randal; Fort, Gersende; Moulines, Eric; Soulier, Philippe. Practical drift conditions for subgeometric rates of convergence. Ann. Appl. Probab. 14 (2004), no. 3, 1353--1377. doi:10.1214/105051604000000323. https://projecteuclid.org/euclid.aoap/1089736288


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