Probability Theory
Quasi-invariant measures on the path space of a diffusion
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
Bell, Denis 1

1 Department of Mathematics, University of North Florida, 4567, St. Johns Bluff Road South, Jacksonville, FL 32224, USA
@article{CRMATH_2006__343_3_197_0,
     author = {Bell, Denis},
     title = {Quasi-invariant measures on the path space of a diffusion},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {197--200},
     publisher = {Elsevier},
     volume = {343},
     number = {3},
     year = {2006},
     doi = {10.1016/j.crma.2006.06.026},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2006.06.026/}
}
TY  - JOUR
AU  - Bell, Denis
TI  - Quasi-invariant measures on the path space of a diffusion
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 197
EP  - 200
VL  - 343
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2006.06.026/
DO  - 10.1016/j.crma.2006.06.026
LA  - en
ID  - CRMATH_2006__343_3_197_0
ER  - 
%0 Journal Article
%A Bell, Denis
%T Quasi-invariant measures on the path space of a diffusion
%J Comptes Rendus. Mathématique
%D 2006
%P 197-200
%V 343
%N 3
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2006.06.026/
%R 10.1016/j.crma.2006.06.026
%G en
%F CRMATH_2006__343_3_197_0
Bell, Denis. 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. http://www.numdam.org/articles/10.1016/j.crma.2006.06.026/

[1] Bell, D. Divergence theorems in path space, J. Funct. Anal., Volume 218 (2005) no. 1, pp. 130-149

[2] Bell, D. Divergence theorems in path space II: degenerate diffusions, C. R. Acad. Sci. Paris, Ser. I, Volume 342 (2006), pp. 869-872

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

[4] Cruzeiro, A.B. Équations différentielles sur l'espace de Wiener et formules de Cameron–Martin non-linéaires, J. Funct. Anal., Volume 54 (1983), pp. 206-227

[5] Driver, B. A Cameron–Martin type quasi-invariance theorem for Brownian motion on a compact manifold, J. Funct. Anal., Volume 109 (1992), pp. 272-376

[6] Hsu, E.P. Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold, J. Funct. Anal., Volume 134 (1995), pp. 417-450

[7] Hu, Y.; Üstünel, A.S.; Zakai, M. Tangent processes on Wiener space, J. Funct. Anal., Volume 192 (2002) no. 1, pp. 234-270

Cited by Sources: