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Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces


 
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1. Title Title of document Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces
 
2. Creator Author's name, affiliation, country Mireille Capitaine; Universite Paul-Sabatier
 
2. Creator Author's name, affiliation, country Elton P. Hsu; Northwestern University
 
2. Creator Author's name, affiliation, country Michel Ledoux; Universite Paul-Sabatier
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Martingale representation, logarithmic Sobolev inequality, Brownian motion, Riemannian manifold
 
3. Subject Subject classification 58G32
 
4. Description 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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7. Date (YYYY-MM-DD) 1997-12-15
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/986
 
10. Identifier Digital Object Identifier 10.1214/ECP.v2-986
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 2
 
12. Language English=en en
 
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