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Shy couplings
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  • Published: 07 November 2006

Shy couplings

  • Itai Benjamini1,
  • Krzysztof Burdzy2 &
  • Zhen-Qing Chen2 

Probability Theory and Related Fields volume 137, pages 345–377 (2007)Cite this article

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  • 10 Citations

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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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel

    Itai Benjamini

  2. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350, USA

    Krzysztof Burdzy & Zhen-Qing Chen

Authors
  1. Itai Benjamini
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  2. Krzysztof Burdzy
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  3. Zhen-Qing Chen
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Corresponding author

Correspondence to Krzysztof Burdzy.

Additional information

Research partially supported by NSF grant DMS-0303310 (KB and ZC).

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Cite this article

Benjamini, I., Burdzy, K. & Chen, ZQ. Shy couplings. Probab. Theory Relat. Fields 137, 345–377 (2007). https://doi.org/10.1007/s00440-006-0008-3

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  • Received: 24 September 2005

  • Revised: 21 February 2006

  • Published: 07 November 2006

  • Issue Date: March 2007

  • DOI: https://doi.org/10.1007/s00440-006-0008-3

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Keywords

  • Brownian Motion
  • Line Segment
  • Markov Process
  • Convex Domain
  • Exit Time
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