ON COLLISIONS OF BROWNIAN PARTICLES

• 成果类型: Article
• 署名作者: Ichiba, Tomoyuki; Karatzas, Ioannis
• 署名单位: University of California System; University of California Santa Barbara
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP641
• 发表日期: 2010
• 页码: 951-977
• 关键词: motion; DIFFUSIONS; coefficients; reflection; uniqueness; wedge

摘要

We examine the behavior of n Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient conditions are established for the absence and for the presence of triple collisions among the particles. As an application to the Atlas model for equity markets, we study a special construction of such systems of diffusing particles using Brownian motions with reflection on polyhedral domains.