HYDRODYNAMIC LIMITS AND PROPAGATION OF CHAOS FOR INTERACTING RANDOM WALKS IN DOMAINS

• 成果类型: Article
• 署名作者: Chen, Zhen-Qing; Fan, Wai-Tong (Louis)
• 署名单位: University of Washington; University of Washington Seattle; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1208
• 发表日期: 2017
• 页码: 1299-1371
• 关键词: chemical-reactions; particle-systems; brownian-motion; markov-chains; diffusion; equation; MODEL; approximations; fluctuations; discrete

摘要

A new non-conservative stochastic reaction diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in this paper. Such a system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. We show that in the macroscopic limit, the particle densities converge to the solution of a coupled nonlinear heat equations. For this, we first prove that propagation of-chaos holds by establishing the uniqueness of a new BBGKY hierarchy. A local central limit theorem for reflected diffusions in bounded Lipschitz domains is also established as a crucial tool.