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 Electronic Communications in Probability > Vol. 2 (1997) > Paper 7 open journal systems 


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

Mireille Capitaine, Universite Paul-Sabatier
Elton P. Hsu, Northwestern University
Michel Ledoux, Universite Paul-Sabatier


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.


Full text: PDF

Pages: 71-81

Published on: December 15, 1997
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Electronic Communications in Probability. ISSN: 1083-589X