Probability Theory
Divergence theorems in path space II: degenerate diffusions
Comptes Rendus. Mathématique, Volume 342 (2006) no. 11, pp. 869-872.

Let x denote an elliptic diffusion process defined on a smooth compact manifold M. In a previous work, we introduced a class of vector fields on the path space of x and studied the admissibility of this class of vector fields with respect to the law of x. In the present Note, we extend this study to the case of degenerate diffusions.

Soit x une diffusion elliptique définie sur une variété compacte régulière M. Dans un travail précédent, nous avons introduit une classe de champs de vecteurs sur l'espace de chemins de x et nous avons étudié l'admissibilité de cette classe de champs de vecteur par rapport à la loi de x. Dans la présente Note, nous étendons cette étude au cas de diffusions dégénérées.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.03.029
Bell, Denis 1

1 Department of Mathematics, University of North Florida, 4567 St. Johns Bluff Road South, Jacksonville, FL 32224, USA
@article{CRMATH_2006__342_11_869_0,
     author = {Bell, Denis},
     title = {Divergence theorems in path space {II:} degenerate diffusions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {869--872},
     publisher = {Elsevier},
     volume = {342},
     number = {11},
     year = {2006},
     doi = {10.1016/j.crma.2006.03.029},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2006.03.029/}
}
TY  - JOUR
AU  - Bell, Denis
TI  - Divergence theorems in path space II: degenerate diffusions
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 869
EP  - 872
VL  - 342
IS  - 11
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2006.03.029/
DO  - 10.1016/j.crma.2006.03.029
LA  - en
ID  - CRMATH_2006__342_11_869_0
ER  - 
%0 Journal Article
%A Bell, Denis
%T Divergence theorems in path space II: degenerate diffusions
%J Comptes Rendus. Mathématique
%D 2006
%P 869-872
%V 342
%N 11
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2006.03.029/
%R 10.1016/j.crma.2006.03.029
%G en
%F CRMATH_2006__342_11_869_0
Bell, Denis. Divergence theorems in path space II: degenerate diffusions. Comptes Rendus. Mathématique, Volume 342 (2006) no. 11, pp. 869-872. doi : 10.1016/j.crma.2006.03.029. http://www.numdam.org/articles/10.1016/j.crma.2006.03.029/

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

[2] Bell, D.; Mohammed, S. An extension of Hörmander's theorem for infinitely degenerate second-order operators, Duke Math. J., Volume 78 (1995) no. 3, pp. 453-475

[3] 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

[4] Elworthy, K.D.; Le Jan, Y.; Li, X.-M. On the Geometry of Diffusion Operators and Stochastic Flows, Lecture Notes in Math., vol. 1720, Springer-Verlag, 1999

[5] Jones, J.D.S.; Léandre, R. Lp-Chen forms on loop spaces, Stochastic Analysis (Durham, 1990), London Math. Soc. Lecture Note Ser., vol. 167, Cambridge Univ. Press, 1991, pp. 103-162

[6] Kusuoka, S.; Stroock, D. Applications of the Malliavin calculus II, J. Fac. Sci. Univ. Tokyo, Volume 32 (1985), pp. 1-76

[7] Léandre, R. Appliquations quantitatives et qualitatives du Calcul de Malliavin, Lecture Notes in Math., vol. 1322, Springer-Verlag, 1988, pp. 109-133

[8] Malliavin, P. Stochastic calculus of variations and hypoelliptic operators, Proceedings of the International Conference on Stochastic Differential Equations, Kinokuniya and Wiley, Kyoto, 1976, pp. 195-263

Cited by Sources: