HYDRODYNAMIC LIMIT AND PROPAGATION OF CHAOS FOR BROWNIAN PARTICLES REFLECTING FROM A NEWTONIAN BARRIER

• 成果类型: Article
• 署名作者: Barnes, Clayton L.
• 署名单位: Technion Israel Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1536
• 发表日期: 2020
• 页码: 1582-1613
• 关键词: free-boundary problems; systems

摘要

In 2001, Frank Knight constructed a stochastic process modeling the one-dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion, and the other particle being Brownian. We construct a multi-particle analog, using Skorohod map estimates in proving a propagation of chaos, and characterizing the hydrodynamic limit as the solution to a PDE with free boundary condition. This PDE resembles the Stefan problem but has a Neumann type boundary condition. Stochastic methods are used to show existence and uniqueness for this free boundary problem.