Segregating Markov Chains
Hirscher, Timo LU
and Martinsson, Anders
LU
(2018)
In Journal of Theoretical Probability
31(3).
p.1512-1538
- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/b508cbae-4292-417e-909b-3ceb7dbad571
- author
- Hirscher, Timo
LU
and Martinsson, Anders
LU
- publishing date
- 2018-09-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Coupling inequality, Markov chain, Non-Markovian coupling, Total variation distance
- in
- Journal of Theoretical Probability
- volume
- 31
- issue
- 3
- pages
- 27 pages
- publisher
- Springer
- external identifiers
-
- scopus:85016408803
- ISSN
- 0894-9840
- DOI
- 10.1007/s10959-017-0743-7
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2017, The Author(s).
- id
- b508cbae-4292-417e-909b-3ceb7dbad571
- date added to LUP
- 2023-12-14 13:21:26
- date last changed
- 2023-12-14 15:39:08
@article{b508cbae-4292-417e-909b-3ceb7dbad571,
abstract = {{<p>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.</p>}},
author = {{Hirscher, Timo and Martinsson, Anders}},
issn = {{0894-9840}},
keywords = {{Coupling inequality; Markov chain; Non-Markovian coupling; Total variation distance}},
language = {{eng}},
month = {{09}},
number = {{3}},
pages = {{1512--1538}},
publisher = {{Springer}},
series = {{Journal of Theoretical Probability}},
title = {{Segregating Markov Chains}},
url = {{http://dx.doi.org/10.1007/s10959-017-0743-7}},
doi = {{10.1007/s10959-017-0743-7}},
volume = {{31}},
year = {{2018}},
}