Coalescence of synchronous couplings |
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| Authors: | Krzysztof Burdzy Zhen-Qing Chen |
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| Affiliation: | (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 |
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| 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. Received: 2 March 2001 / Revised version: 6 March 2001 / Published online: 1 July 2002 |
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