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

โœ Scribed by E.P. Hsu

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
957 KB
Volume
134
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

We study a quasi-invariance property of the Wiener measure on the path space over a compact Riemannian manifold which generalizes the well-known CameronMartin 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. 'c. 1995 Academic Press, Inc.

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