Comptes Rendus
no. 3
Probability Theory
Quasi-invariant measures on the path space of a diffusion

Presented by: Paul Malliavin

Denis Bell1
1 Department of Mathematics, University of North Florida, 4567, St. Johns Bluff Road South, Jacksonville, FL 32224, USA
Comptes Rendus. Mathématique, Volume 343 (2006) no. 3, pp. 197-200.

The author has previously constructed a class of admissible vector fields on the path space of an elliptic diffusion process x taking values in a closed compact manifold. In this Note the existence of flows for this class of vector fields is established and it is shown that the law of x is quasi-invariant under these flows.

L'auteur a précédemment construit une classe de champs de vecteurs admissibles sur l'espace des chemins d'une diffusion elliptique x prenant valeurs dans une variété compacte fermée. Dans cette Note l'existence des flots pour cette classe de champs de vecteurs est établie et on montre que la loi de x est quasi-invariante sous ces flots.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.06.026

Denis Bell 1

1 Department of Mathematics, University of North Florida, 4567, St. Johns Bluff Road South, Jacksonville, FL 32224, USA 
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Denis Bell. Quasi-invariant measures on the path space of a diffusion. Comptes Rendus. Mathématique, Volume 343 (2006) no. 3, pp. 197-200. doi : 10.1016/j.crma.2006.06.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.06.026/

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[3] D. Bell, Admissible vector fields and quasi-invariant measures. Appendix to The Malliavin Calculus, second ed., Dover Publications, Mineola, NY, 2006

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