Levy area for the free Brownian motion: existence and non-existence

被引：11

作者：

Victoir, N ^{[1
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX1 3LB, England

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2004年 / 208卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

free Brownian motion; rough paths; Burkholder-Davis-Gundy inequality; tensor product;

D O I：

10.1016/S0022-1236(03)00063-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This note extends the work of Capitaine (J. Funct. Anal. 179 (1) (2001) 153) on the Levy area process for the free Brownian motion in two directions. First, we reprove that a Levy area for the Free Brownian motion exists in the Von Neumann tensor product, by exhibiting a non-commutative Burkholder-Davis-Gundytype inequality. Then, we show that there does not exist a Levy area in the projective tensor product. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：107 / 121

页数：15

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