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Quantitative Convergence Rates for Subgeometric Markov Chains

Part of: Markov processes

Published online by Cambridge University Press:  30 January 2018

Christophe Andrieu ,
Gersende Fort  and
Matti Vihola
Christophe Andrieu*
Affiliation:
University of Bristol
Gersende Fort*
Affiliation:
CNRS and Télécom ParisTech
Matti Vihola*
Affiliation:
University of Jyväskylä
*
∗ Postal address: School of Mathematics, University of Bristol, Bristol BS8 1TW, UK.
∗∗ Postal address: Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France.
∗∗∗ Postal address: Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35, Jyväskylä, FI-40014, Finland Email address: matti.s.vihola@jyu.fi
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Abstract

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We provide explicit expressions for the constants involved in the characterisation of ergodicity of subgeometric Markov chains. The constants are determined in terms of those appearing in the assumed drift and one-step minorisation conditions. The results are fundamental for the study of some algorithms where uniform bounds for these constants are needed for a family of Markov kernels. Our results accommodate also some classes of inhomogeneous chains.

Keywords

Markov chaininhomogeneoussubgeometric ergodicitypolynomial ergodicity

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60J22: Computational methods in Markov chains

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 391 - 404
Copyright
© Applied Probability Trust 

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