Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 2 (1997), paper no. 7, 71-81.
Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces
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.
Electron. Commun. Probab., Volume 2 (1997), paper no. 7, 71-81.
Accepted: 15 December 1997
First available in Project Euclid: 26 January 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
This work is licensed under aCreative Commons Attribution 3.0 License.
Capitaine, Mireille; Hsu, Elton; Ledoux, Michel. Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces. Electron. Commun. Probab. 2 (1997), paper no. 7, 71--81. doi:10.1214/ECP.v2-986. https://projecteuclid.org/euclid.ecp/1453832502