Segregating Markov Chains

Timo Hirscher () and Anders Martinsson ()
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Timo Hirscher: Chalmers University of Technology
Anders Martinsson: Chalmers University of Technology

Journal of Theoretical Probability, 2018, vol. 31, issue 3, 1512-1538

Abstract: 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 $$\tfrac{1}{2}$$ 1 2 .

Keywords: Markov chain; Non-Markovian coupling; Total variation distance; Coupling inequality; Primary 60J10; Secondary 60C05 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-017-0743-7

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