Burdzy, KrzysztofChen, Zhen-Qing2005-11-302005-11-302002-08Burdzy, K. & Z.Q. Chen. (2002). Coalescence of synchronous couplings. Probability Theory and Related Fields, 123(4), 553-578.http://hdl.handle.net/1773/2219We 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 1.257348 bytesapplication/pdfen-USReflected Brownian motioncouplingLipschitz domainArticle