Shy couplings

Itai Benjamini; Krzysztof Burdzy; Zhen Qing Chen

doi:10.1007/s00440-006-0008-3

Shy couplings

Itai Benjamini, Krzysztof Burdzy^*, Zhen Qing Chen

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

A pair (X, Y) of Markov processes on a metric space is called a Markov coupling if X and Y have the same transition probabilities and (X, Y) is a Markov process. We say that a coupling is "shy" if inf _{t ≥ 0} dist(X _t, Y _t) ≥ 0 with positive probability. We investigate whether shy couplings exist for several classes of Markov processes.

Original language	English
Pages (from-to)	345-377
Number of pages	33
Journal	Probability Theory and Related Fields
Volume	137
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-006-0008-3
Publication status	Published - Mar 2007
Externally published	Yes

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10.1007/s00440-006-0008-3

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Benjamini, I., Burdzy, K., & Chen, Z. Q. (2007). Shy couplings. Probability Theory and Related Fields, 137(3-4), 345-377. https://doi.org/10.1007/s00440-006-0008-3

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AU - Burdzy, Krzysztof

AU - Chen, Zhen Qing

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AB - A pair (X, Y) of Markov processes on a metric space is called a Markov coupling if X and Y have the same transition probabilities and (X, Y) is a Markov process. We say that a coupling is "shy" if inf t ≥ 0 dist(X t, Y t) ≥ 0 with positive probability. We investigate whether shy couplings exist for several classes of Markov processes.

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Shy couplings

Abstract

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