Stochastic calculus with respect to free Brownian motion and analysis on Wigner space

被引：120

作者：

Biane, P

Speicher, R

机构：

[1] CNRS, DMI, Ecole Normale Super, F-75005 Paris, France

[2] Univ Heidelberg, Inst Angew Math, D-69120 Heidelberg, Germany

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1998年 / 112卷 / 03期

关键词：

D O I：

10.1007/s004400050194

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：

We define stochastic integrals with respect to free Brownian motion, and show that they satisfy Burkholder-Gundy type inequalities in operator norm. We prove also a version of Ito's predictable representation theorem, as well as product form and functional form of Ito's formula. Finally we develop stochastic analysis on the free Fock space, in analogy with stochastic analysis on the Wiener space.

引用

页码：373 / 409

页数：37

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