UNSPECIFIED (2000) Efficient Markovian couplings: Examples and counterexamples. ANNALS OF APPLIED PROBABILITY, 10 (2). pp. 362-409. ISSN 1050-5164

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Abstract

In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the spectral gap. This notion is of interest not only for its own sake, but also of growing importance arising from the recent advent of methods of "perfect simulation": it helps to establish the "price of perfection" for such methods. In general, one can always achieve efficient coupling if the coupling is allowed to "cheat" (if each component's behavior is affected by the future behavior of the other component), but the situation is more interesting if the coupling is required to be co-adapted. We present an informal heuristic for the existence of an efficient coupling, and justify the heuristic by proving rigorous results and examples in the contexts of finite reversible Markov chains and of reflecting Brownian motion in planar domains.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ANNALS OF APPLIED PROBABILITY
Publisher:	INST MATHEMATICAL STATISTICS
ISSN:	1050-5164
Date:	May 2000
Volume:	10
Number:	2
Number of Pages:	48
Page Range:	pp. 362-409
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/12471

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