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 Electronic Journal of Probability > Vol. 5 (2000) > Paper 11 open journal systems 


The Abstract Riemannian Path Space

D. Feyel, Université Evry
A. de La Pradelle, Université Paris VI


Abstract
On the Wiener space $Omega$, we introduce an abstract Ricci process $A_t$ and a pseudo-gradient $Frightarrow{F}^sharp$ 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.


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Pages: 1-17

Published on: May 25, 2000
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Electronic Journal of Probability. ISSN: 1083-6489