Coalescence of synchronous couplings

• 成果类型: Article
• 署名作者: Burdzy, K; Chen, ZQ
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400200202
• 发表日期: 2002
• 页码: 553-578
• 关键词: reflecting brownian-motion; diffusion-processes; domains

摘要

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.