@article{ECP986,
author = {Mireille Capitaine and Elton Hsu and Michel Ledoux},
title = {Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {2},
year = {1997},
keywords = {Martingale representation, logarithmic Sobolev inequality, Brownian motion, Riemannian manifold},
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.},
pages = {no. 7, 71-81},
issn = {1083-589X},
doi = {10.1214/ECP.v2-986},
url = {http://ecp.ejpecp.org/article/view/986}}