The Abstract Riemannian Path Space

D. Feyel (Université Evry)
A. de La Pradelle (Université Paris VI)


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.

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Pages: 1-17

Publication Date: May 25, 2000

DOI: 10.1214/EJP.v5-67


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