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Coalescence of synchronous couplings
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  • Published: August 2002

Coalescence of synchronous couplings

  • Krzysztof Burdzy1 &
  • Zhen-Qing Chen1 

Probability Theory and Related Fields volume 123, pages 553–578 (2002)Cite this article

Abstract.

 We consider a pair of reflected Brownian motions in a Lipschitz planar domain starting from different points but driven by the same Brownian motion. First we construct such a pair of processes in a certain weak sense, since it is not known whether a strong solution to the Skorohod equation in Lipschitz domains exists. Then we prove that the distance between the two processes converges to zero with probability one if the domain has a polygonal boundary or it is a ``lip domain'', i.e., a domain between the graphs of two Lipschitz functions with Lipschitz constants strictly less than 1.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA. e-mail burdzy@math.washington.edu, http://www.math.washington.edu/~burdzy/; zchen@math.washington.edu, http://www.math.washington.edu/~zchen/, , , , , , US

    Krzysztof Burdzy & Zhen-Qing Chen

Authors
  1. Krzysztof Burdzy
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  2. Zhen-Qing Chen
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Received: 2 March 2001 / Revised version: 6 March 2001 / Published online: 1 July 2002

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Burdzy, K., Chen, ZQ. Coalescence of synchronous couplings. Probab Theory Relat Fields 123, 553–578 (2002). https://doi.org/10.1007/s004400200202

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  • Issue Date: August 2002

  • DOI: https://doi.org/10.1007/s004400200202

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Keywords

  • Brownian Motion
  • Strong Solution
  • Lipschitz Function
  • Lipschitz Constant
  • Lipschitz Domain
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