Quasi-Invariance of the Wiener Measure on the Path Space over a Compact Riemannian Manifold

Elton P. Hsu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Scopus citations

Abstract

We study a quasi-invariance property of the Wiener measure on the path space over a compact Riemannian manifold which generalizes the well-known Cameron-Martin theorem for euclidean space. This property is used to prove an integration by parts formula for the gradient operator. We use the integration by parts formula to compute explicitly the Ornstein-Uhlenbeck operator in the path space.

Original languageEnglish (US)
Pages (from-to)417-450
Number of pages34
JournalJournal of Functional Analysis
Volume134
Issue number2
DOIs
StatePublished - 1995

ASJC Scopus subject areas

  • Analysis

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