On Free Stochastic Differential Equations

被引：10

作者：

Kargin, Vladislav ^{[1
]}

机构：

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

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2011年 / 24卷 / 03期

关键词：

Free probability; Stochastic differential equations;

D O I：

10.1007/s10959-011-0341-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：

The paper derives an equation for the Cauchy transform of the solution of a free stochastic differential equation (SDE). This new equation is used to solve several particular examples of free SDEs.

引用

页码：821 / 848

页数：28

共 13 条

[1]

[Anonymous], APPL MATH SCI

[2]

[Anonymous], 2006, LECT COMBINATORICS F, DOI DOI 10.1017/CBO9780511735127

[3]

[Anonymous], 1992, CRM MONOGRAPH SERIES

[4] Ito formula for free stochastic integrals [J].

Anshelevich, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 188 (01) :292-315

[5] Stochastic calculus with respect to free Brownian motion and analysis on Wigner space [J].

Biane, P ;

Speicher, R .

PROBABILITY THEORY AND RELATED FIELDS, 1998, 112 (03) :373-409

[6] Free diffusions, free entropy and free Fisher information [J].

Biane, P ;

Speicher, R .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2001, 37 (05) :581-606

[7]

Biane P., 1997, Fields Inst. Commun., V12, P1

[8] Free Wishart processes [J].

Capitaine, M ;

Donati-Martin, C .

JOURNAL OF THEORETICAL PROBABILITY, 2005, 18 (02) :413-438

[9] Free Jacobi process [J].

Demni, N. .

JOURNAL OF THEORETICAL PROBABILITY, 2008, 21 (01) :118-143

[10] Free Orstein-Uhlenbeck processes [J].

Gao, Mingchu .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 322 (01) :177-192

← 1 2 →