Open Access
2000 The Abstract Riemannian Path Space
D. Feyel, A. de La Pradelle
Author Affiliations +
Electron. J. Probab. 5: 1-17 (2000). DOI: 10.1214/EJP.v5-67


On the Wiener space $\Omega$, we introduce an abstract Ricci process $A_t$ and a pseudo-gradient $F\rightarrow{F}^\sharp$ which are compatible through an integration by parts formula. They give rise to a $\sharp$-Sobolev space on $\Omega$, logarithmic Sobolev inequalities, and capacities, which are tight on Hoelder compact sets of $\Omega$. These are then applied to the path space over a Riemannian manifold.


Download Citation

D. Feyel. A. de La Pradelle. "The Abstract Riemannian Path Space." Electron. J. Probab. 5 1 - 17, 2000.


Accepted: 25 May 2000; Published: 2000
First available in Project Euclid: 7 March 2016

zbMATH: 0949.60064
MathSciNet: MR1781023
Digital Object Identifier: 10.1214/EJP.v5-67

Primary: 60H07
Secondary: 58D20 , 58J99 , 60H10 , 60H25

Keywords: Bismut-Driver formula , Capacities , Logarithmic Sobolev inequality , Riemannian manifold path space , Sobolev Spaces , Wiener space

Vol.5 • 2000
Back to Top