HOMOGENIZATION AND PROPAGATION OF CHAOS TO A NONLINEAR DIFFUSION WITH STICKY REFLECTION

• 成果类型: Article
• 署名作者: GRAHAM, C
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01200497
• 发表日期: 1995
• 页码: 291-302
• 关键词: boundary

摘要

We study a process reflecting in a domain. The process follows Wentzell non-sticky boundary conditions while being adsorbed at the boundary at a certain rate with respect to local time and desorbed at a rate with respect to natural time. We show that when the rates go to infinity with a converging ratio, the process converges to a process with sticky reflection having the limit ratio as the sojourn coefficient. We then study a mean-field interacting system of such particles. We show propagation of chaos to a nonlinear diffusion with sticky reflection when we perform this homogenization simultaneously as the number of particles goes to infinity.