Journal of Applied Probability

Quantitative convergence rates for subgeometric Markov chains

Christophe Andrieu, Gersende Fort, and Matti Vihola

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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.

Article information

Source
J. Appl. Probab., Volume 52, Number 2 (2015), 391-404.

Dates
First available in Project Euclid: 23 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1437658605

Digital Object Identifier
doi:10.1239/jap/1437658605

Mathematical Reviews number (MathSciNet)
MR3372082

Zentralblatt MATH identifier
1323.60090

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60J22: Computational methods in Markov chains [See also 65C40]

Keywords
Markov chain inhomogeneous subgeometric ergodicity polynomial ergodicity

Citation

Andrieu, Christophe; Fort, Gersende; Vihola, Matti. Quantitative convergence rates for subgeometric Markov chains. J. Appl. Probab. 52 (2015), no. 2, 391--404. doi:10.1239/jap/1437658605. https://projecteuclid.org/euclid.jap/1437658605


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References

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