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The Abstract Riemannian Path Space

   
@article{EJP67,
	author = {D. Feyel and A. de La Pradelle},
	title = {The Abstract Riemannian Path Space},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {5},
	year = {2000},
	keywords = {Wiener space, Sobolev spaces, Bismut-Driver formula, Logarithmic Sobolev inequality, Capacities, Riemannian manifold path space.},
	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.},
	pages = {no. 11, 1-17},
	issn = {1083-6489},
	doi = {10.1214/EJP.v5-67},    
        url = {http://ejp.ejpecp.org/article/view/67}}