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Quantitative Convergence Rates for Subgeometric Markov Chains

  • Christophe Andrieu (a1), Gersende Fort (a2) and Matti Vihola (a3)
Abstract

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.

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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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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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