The divergence of Banach space valued random variables on Wiener space

被引：8

作者：

Mayer-Wolf, E ^{[1
]}

Zakai, M

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[2] Technion Israel Inst Technol, Dept Elect Engn, IL-32000 Haifa, Israel

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2005年 / 132卷 / 02期

关键词：

abstract Wiener space; divergence; flows;

D O I：

10.1007/s00440-004-0397-0

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 domain of definition of the divergence operator delta on an abstract Wiener space (W, H, mu) is extended to include W - valued and W x W - valued "integrands". The main properties and characterizations of this extension are derived and it is shown that in some sense the added elements in delta' s extended domain have divergence zero. These results are then applied to the analysis of quasiinvariant flows induced by W-valued vector fields and, among other results, it turns out that these divergence-free vector fields "are responsible" for generating measure preserving flows.

引用

页码：291 / 320

页数：30

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