Quasi-invariance of the Wiener measure on path spaces: Noncompact case

被引：0

作者：

Hsu, EP ^{[1
]}

机构：

[1] Northwestern Univ, Dept Math, Evanston, IL 60208 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2002年 / 193卷 / 02期

基金：

美国国家科学基金会;

关键词：

path space; Wiener measure; Cameron-Martin vector fields; quasi-invariance;

D O I：

10.1006/jfan.2001.3940

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a geometrically and stochastically complete, noncompact Riemannian manifold, we show that the flows on the path space generated by the Cameron-Martin vector fields exist as a set of random variables. Furthermore, if the Ricci curvature grows at most linearly, then the Wiener measure (the law of Brownian motion on the manifold) is quasi-invariant under these flows. (C) 2002 Elsevier Science (USA).

引用

页码：278 / 290

页数：13

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