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1997 Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces
Mireille Capitaine, Elton Hsu, Michel Ledoux
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Electron. Commun. Probab. 2: 71-81 (1997). DOI: 10.1214/ECP.v2-986

Abstract

We show how the Clark-Ocone-Haussmann formula for Brownian motion on a compact Riemannian manifold put forward by S. Fang in his proof of the spectral gap inequality for the Ornstein-Uhlenbeck operator on the path space can yield in a very simple way the logarithmic Sobolev inequality on the same space. By an appropriate integration by parts formula the proof also yields in the same way a logarithmic Sobolev inequality for the path space equipped with a general diffusion measure as long as the torsion of the corresponding Riemannian connection satisfies Driver's total antisymmetry condition.

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Mireille Capitaine. Elton Hsu. Michel Ledoux. "Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces." Electron. Commun. Probab. 2 71 - 81, 1997. https://doi.org/10.1214/ECP.v2-986

Information

Accepted: 15 December 1997; Published: 1997
First available in Project Euclid: 26 January 2016

zbMATH: 0890.60045
MathSciNet: MR1484557
Digital Object Identifier: 10.1214/ECP.v2-986

Subjects:
Primary: 58G32

JOURNAL ARTICLE
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