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Faithful Couplings of Markov Chains: Now Equals Forever

✍ Scribed by Jeffrey S. Rosenthal

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
173 KB
Volume
18
Category
Article
ISSN
0196-8858

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✦ Synopsis

This short note considers the usual coupling approach to bounding convergence of Markov chains. It addresses the question of whether it suffices to have two chains become equal at a single time or whether it is necessary to have them then remain equal for all future times. Ε½ . Let P x, ΠΈ be the transition probabilities for a Markov chain on a Polish state space X X. Let and be two initial distributions for the chain. This paper is related to the problem of bounding the total variation 5 k k 5 < k Ε½ . k Ε½ .< distance P y P s sup P A y P A , after k steps, be-

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