Infinite dimensional stochastic differential equations for Dyson's model

被引：20

作者：

Tsai, Li-Cheng ^{[1
]}

机构：

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2016年 / 166卷 / 3-4期

关键词：

Dyson's Brownian motion; Dyson's model; Stochastic differential equations; Infinite-dimensional; Strong existence; Pathwise uniqueness; Correlation function; WIENER PROCESSES;

D O I：

10.1007/s00440-015-0672-2

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：801 / 850

页数：50

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