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

被引：0
|
作者：
Philippe Biane
Roland Speicher
机构：
[1] CNRS,
[2] DMI,undefined
[3] Ecole Normale Supérieure,undefined
[4] 45,undefined
[5] rue d'Ulm,undefined
[6] 75005 Paris,undefined
[7] France. e-mail: biane@dmi.ens,undefined
[8] fr,undefined
[9] Institut für Angewandte Mathematik,undefined
[10] Universität Heidelberg,undefined
[11] Im Neuenheimer Feld 294,undefined
[12] D-69120 Heidelberg,undefined
[13] Germany. e-mail: roland.Speicher@urz.uni-heidelberg.de,undefined
来源：
Probability Theory and Related Fields | 1998年 / 112卷
关键词：
Mathematics Subject Classification (1991): 60H05; 46L50; 81S25;
D O I：
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中图分类号：
学科分类号：
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 Itô's predictable representation theorem, as well as product form and functional form of Itô's formula. Finally we develop stochastic analysis on the free Fock space, in analogy with stochastic analysis on the Wiener space.
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页码：373 / 409
页数：36
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