Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold
type: Item
instance of: scholarly article
title: Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold
zbMATH Open document ID: 0847.58082
author: Elton P. Hsu
published in: Journal of Functional Analysis
publication date: 1996-10-14T00:00:00Z
review text: The quasi-invariance property of the Wiener measure in the flat Euclidean space is the well known Cameron-Martin theorem. For Brownian motion on a compact Riemannian manifold significant results on the quasi-invariance of the flow on the path space are due to \textit{B. K. Driver} [J. Funct. Anal. 110, No. 2, 272-376 (1992; Zbl 0765.60064)]. This property is utilized to show that the directional derivative and gradient operators are closable, together with the associated Dirichlet form. The integration by parts formula is proved and used to compute explicitly the Ornstein-Uhlen-Beck operator in the path space, and to show that the set of cylindrical functions lies in its domain of definition.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 850628
zbMATH Keywords: stochastic analysis on manifolds
zbMATH Keywords: quasi-invariance
zbMATH Keywords: Wiener measure
zbMATH Keywords: path space
zbMATH Keywords: Ornstein-Uhlen-Beck operator
MaRDI profile type: Publication
full work available at URL: jfan.1995.1152
OpenAlex ID: W4210731678
DOI: 10.1006/JFAN.1995.1152
description: scientific article; zbMATH DE number 850628