Quantitative convergence rates for sub-geometric Markov chains

Christophe Andrieu; Gersende Fort; Matti Vihola

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arXiv · 1309.0622

Quantitative convergence rates for sub-geometric Markov chains

Christophe Andrieu·Gersende Fort·Matti Vihola

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Abstract

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

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Christophe Andrieu, Gersende Fort, Matti Vihola. 2014-03-17. Quantitative convergence rates for sub-geometric Markov chains. https://arxiv.org/abs/1309.0622

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