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Quasi-Invariance of the Wiener Measure on Path Spaces: Noncompact Case

✍ Scribed by Elton P. Hsu

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 138 KB
Volume: 193
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3940

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✦ Synopsis

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. # 2002 Elsevier Science (USA)

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