Strong solutions of stochastic equations with rank-based coefficients

• 成果类型: Article
• 署名作者: Ichiba, Tomoyuki; Karatzas, Ioannis; Shkolnikov, Mykhaylo
• 署名单位: University of California System; University of California Santa Barbara; Columbia University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0426-3
• 发表日期: 2013
• 页码: 229-248
• 关键词: brownian-motion; DIFFUSIONS; collisions

摘要

We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We show that strong existence and uniqueness hold until the first time three particles collide. Motivated by this result, we improve significantly the existing conditions for the absence of such triple collisions in the case of finite-dimensional systems, and provide the first condition of this type for systems with a countable infinity of particles.