Segregating Markov Chains

Timo Hirscher; Anders Martinsson

doi:10.1007/s10959-017-0743-7

Segregating Markov Chains

Research output: Contribution to journal › Article › peer-review

Abstract

Dealing with finite Markov chains in discrete time, the focus often lies on convergence behavior and one tries to make different copies of the chain meet as fast as possible and then stick together. There are, however, discrete finite (reducible) Markov chains, for which two copies started in different states can be coupled to meet almost surely in finite time, yet their distributions keep a total variation distance bounded away from 0, even in the limit as time tends to infinity. We show that the supremum of total variation distance kept in this context is 12.

Original language	English
Pages (from-to)	1512-1538
Number of pages	27
Journal	Journal of Theoretical Probability
Volume	31
Issue number	3
DOIs	https://doi.org/10.1007/s10959-017-0743-7
Publication status	Published - 2018 Sept 1
Externally published	Yes

Subject classification (UKÄ)

Probability Theory and Statistics

Free keywords

Coupling inequality
Markov chain
Non-Markovian coupling
Total variation distance

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10.1007/s10959-017-0743-7

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AB - Dealing with finite Markov chains in discrete time, the focus often lies on convergence behavior and one tries to make different copies of the chain meet as fast as possible and then stick together. There are, however, discrete finite (reducible) Markov chains, for which two copies started in different states can be coupled to meet almost surely in finite time, yet their distributions keep a total variation distance bounded away from 0, even in the limit as time tends to infinity. We show that the supremum of total variation distance kept in this context is 12.

KW - Coupling inequality

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KW - Non-Markovian coupling

KW - Total variation distance

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ER -

Segregating Markov Chains

Abstract

Subject classification (UKÄ)

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