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Mixing and average mixing times for general Markov processes

Part of: Miscellaneous topics in measure theory Real functions: Miscellaneous topics Markov processes

Published online by Cambridge University Press:  14 August 2020

Robert M. Anderson ,
Haosui Duanmu  and
Aaron Smith
Robert M. Anderson
Affiliation:
Department of Economics, University of California, Berkeley, CA e-mail: robert.anderson@berkeley.eduasmi28@uottawa.ca
Haosui Duanmu*
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada
Aaron Smith
Affiliation:
Department of Economics, University of California, Berkeley, CA e-mail: robert.anderson@berkeley.eduasmi28@uottawa.ca
*
e-mail: duanmuhaosui@berkeley.edu
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Abstract

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Yuval Peres and Perla Sousi showed that the mixing times and average mixing times of reversible Markov chains on finite state spaces are equal up to some universal multiplicative constant. We use tools from nonstandard analysis to extend this result to reversible Markov chains on compact state spaces that satisfy the strong Feller property.

Keywords

Markov chainmixing timenonstandard analysisnonstandard representation

MSC classification

Primary: 26E35: Nonstandard analysis
Secondary: 28E05: Nonstandard measure theory 60J05: Discrete-time Markov processes on general state spaces
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 3 , September 2021 , pp. 541 - 552
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Canadian Mathematical Society 2020

References

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