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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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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DOI: https://doi.org/10.1007/s004400200202
Keywords
- Brownian Motion
- Strong Solution
- Lipschitz Function
- Lipschitz Constant
- Lipschitz Domain