Abstract
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.
Citation
D. Feyel. A. de La Pradelle. "The Abstract Riemannian Path Space." Electron. J. Probab. 5 1 - 17, 2000. https://doi.org/10.1214/EJP.v5-67
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