Comptes Rendus
Probability Theory
Error calculus and regularity of Poisson functionals: the lent particle method
Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 779-782.

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

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

Received:
Accepted:
Published online:
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

Cited by Sources:

Comments - Policy