Quasi-invariance of the Wiener measure on the path space over a complete Riemannian manifold

Elton P Hsu; Cheng Ouyang

doi:10.1016/j.jfa.2009.05.017

Quasi-invariance of the Wiener measure on the path space over a complete Riemannian manifold

Elton P Hsu, Cheng Ouyang

Mathematics

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10 Scopus citations

Abstract

We prove a generalization of the Cameron–Martin theorem for a geometrically and stochastically complete Riemannian manifold; namely, the Wiener measure on the path space over such a manifold is quasi-invariant under the flow generated by a Cameron–Martin vector field.

Original language	English
Pages (from-to)	1379
Journal	Journal of Functional Analysis
Volume	257
DOIs	https://doi.org/10.1016/j.jfa.2009.05.017
State	Published - 2009

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title = "Quasi-invariance of the Wiener measure on the path space over a complete Riemannian manifold",

abstract = "We prove a generalization of the Cameron–Martin theorem for a geometrically and stochastically complete Riemannian manifold; namely, the Wiener measure on the path space over such a manifold is quasi-invariant under the flow generated by a Cameron–Martin vector field.",

author = "Hsu, {Elton P} and Cheng Ouyang",

year = "2009",

doi = "10.1016/j.jfa.2009.05.017",

language = "English",

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journal = "Journal of Functional Analysis",

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T1 - Quasi-invariance of the Wiener measure on the path space over a complete Riemannian manifold

AU - Hsu, Elton P

AU - Ouyang, Cheng

PY - 2009

Y1 - 2009

N2 - We prove a generalization of the Cameron–Martin theorem for a geometrically and stochastically complete Riemannian manifold; namely, the Wiener measure on the path space over such a manifold is quasi-invariant under the flow generated by a Cameron–Martin vector field.

AB - We prove a generalization of the Cameron–Martin theorem for a geometrically and stochastically complete Riemannian manifold; namely, the Wiener measure on the path space over such a manifold is quasi-invariant under the flow generated by a Cameron–Martin vector field.

U2 - 10.1016/j.jfa.2009.05.017

DO - 10.1016/j.jfa.2009.05.017

M3 - Article

SN - 0022-1236

VL - 257

SP - 1379

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

ER -

Quasi-invariance of the Wiener measure on the path space over a complete Riemannian manifold

Abstract

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