Comptes Rendus
no. 13-14
Probability Theory
Error calculus and regularity of Poisson functionals: the lent particle method
[Calcul d'erreur et régularité des fonctionnelles de Poisson : la méthode de la particule prêtée]

Présenté par : Paul Malliavin

Nicolas Bouleau1
1 École des Ponts, Paris-Est, ParisTech, 6 et 8, avenue Blaise-Pascal, cité Descartes, Champs-sur-Marne, Marne-la vallée cedex, France
Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 779-782.

Nous proposons une nouvelle méthode pour appliquer le calcul fonctionnel lipschitzien des formes de Dirichlet locales aux mesures aléatoires de Poisson.

We propose a new method to apply the Lipschitz functional calculus of local Dirichlet forms to Poisson random measures.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.05.020
Nicolas Bouleau 1

1 École des Ponts, Paris-Est, ParisTech, 6 et 8, avenue Blaise-Pascal, cité Descartes, Champs-sur-Marne, Marne-la vallée cedex, France 
@article{CRMATH_2008__346_13-14_779_0,
     author = {Nicolas Bouleau},
     title = {Error calculus and regularity of {Poisson} functionals: the lent particle method},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {779--782},
     publisher = {Elsevier},
     volume = {346},
     number = {13-14},
     year = {2008},
     doi = {10.1016/j.crma.2008.05.020},
     language = {en},
}
TY  - JOUR
AU  - Nicolas Bouleau
TI  - Error calculus and regularity of Poisson functionals: the lent particle method
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 779
EP  - 782
VL  - 346
IS  - 13-14
PB  - Elsevier
DO  - 10.1016/j.crma.2008.05.020
LA  - en
ID  - CRMATH_2008__346_13-14_779_0
ER  - 
%0 Journal Article
%A Nicolas Bouleau
%T Error calculus and regularity of Poisson functionals: the lent particle method
%J Comptes Rendus. Mathématique
%D 2008
%P 779-782
%V 346
%N 13-14
%I Elsevier
%R 10.1016/j.crma.2008.05.020
%G en
%F CRMATH_2008__346_13-14_779_0
Nicolas Bouleau. Error calculus and regularity of Poisson functionals: the lent particle method. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 779-782. doi : 10.1016/j.crma.2008.05.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.05.020/

[1] S. Albeverio; Yu.G. Kondratiev; M. Röckner Analysis and geometry on configuration spaces, J. Funct. Anal., Volume 154 (1998) no. 2, pp. 444-500

[2] N. Bouleau Error Calculus for Finance and Physics: The Language of Dirichlet Forms, De Gruyter, 2003

[3] N. Bouleau; F. Hirsch Dirichlet Forms and Analysis on Wiener Space, De Gruyter, 1991

[4] L. Denis A criterion of density for solutions of Poisson-driven SDEs, Probab. Theory Relat. Fields, Volume 118 (2000), pp. 406-426

[5] Y. Ishikawa; H. Kunita Malliavin calculus on the Wiener–Poisson space and its application to canonical SDE with jumps, Stochastic Process. Appl., Volume 116 (2006), pp. 1743-1769

[6] Z.-M. Ma; M. Röckner Construction of diffusions on configuration spaces, Osaka J. Math., Volume 37 (2000), pp. 273-314

[7] D. Nualart; J. Vives Anticipative calculus for the Poisson process based on the Fock space, Sém. Probabilités XXIV, Lecture Notes in Math., vol. 1426, Springer, 1990, pp. 154-165

[8] J. Picard On the existence of smooth densities for jump processes, Probab. Theory Relat. Fields, Volume 105 (1996), pp. 481-511

[9] N. Privault A pointwise equivalence of gradients on configuration spaces, C. R. Acad. Sci. Paris, Volume 327 (1998), pp. 677-682

[10] J.-L. Solé; F. Utzet; J. Vives Canonical Lévy processes and Malliavin calculus, Stochastic Process. Appl., Volume 117 (2007), pp. 165-187

Cité par Sources :

Commentaires - Politique