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Geometric L 2 and L 1 convergence are equivalent for reversible Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Gareth O. Roberts  and
Richard L. Tweedie
Gareth O. Roberts*
Affiliation:
University of Lancaster
Richard L. Tweedie*
Affiliation:
University of Minnesota
*
1 Postal address: Department of Mathematics and Statistics, University of Lancaster, Lancaster LA1 4YF, England. Email: g.o.roberts@lancaster.ac.uk
† Richard Tweedie died 7 June 2001.
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Abstract

The paper proves the statement of the title, and shows that it has useful applications in evaluating the convergence of queueing models and Gibbs samplers with deterministic and random scans.

Keywords

Rates of convergenceMarkov chainGibbs samplerMCMC

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces

Information

Type
Markov chains
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 37 - 41
Copyright
Copyright © Applied Probability Trust 2001 

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