Infinite dimensional stochastic differential equations for Dyson's model

• 成果类型: Article
• 署名作者: Tsai, Li-Cheng
• 署名单位: Stanford University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0672-2
• 发表日期: 2016
• 页码: 801-850
• 关键词: wiener processes

摘要

In this paper we show the strong existence and the pathwise uniqueness of an infinite-dimensional stochastic differential equation (SDE) corresponding to the bulk limit of Dyson's Brownian Motion, for all . Our construction applies to an explicit and general class of initial conditions, including the lattice configuration and the sine process. We further show the convergence of the finite to infinite-dimensional SDE. This convergence concludes the determinantal formula of Katori and Tanemura (Commun Math Phys 293(2):469-497, 2010) for the solution of this SDE at beta=2.