Free Wishart processes

被引：11

作者：

Capitaine, M

Donati-Martin, C

机构：

[1] Univ Toulouse 3, Lab Stat & Probabil, F-31062 Toulouse, France

[2] Univ Paris 06, LPMA, F-75252 Paris, France

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2005年 / 18卷 / 02期

关键词：

free probability; random matrices; Wishart processes;

D O I：

10.1007/s10959-005-3511-z

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：

Using a matrix approach, we define free Wishart processes of parameter lambda > 0 and prove a free additivity property and invertibility for lambda>1. For lambda >= 1. we show that a free Wishart process is a solution of a SDE of square Bessel process type, driven by a free complex Brownian motion. In the case lambda > 1. we establish existence and uniqueness of a strong solution of such a SDE.

引用

页码：413 / 438

页数：26

共 19 条

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[Anonymous], 1969, ALGEBRES OPERATEURS

[2]

Biane P, 1997, INDIANA U MATH J, V46, P705

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