Probability Theory
Error calculus and regularity of Poisson functionals: the lent particle method

Presented by: Paul Malliavin

Bouleau, Nicolas1
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.

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
Bouleau, Nicolas 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 = {Bouleau, Nicolas},
     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},
     url = {https://www.numdam.org/articles/10.1016/j.crma.2008.05.020/}
}
TY  - JOUR
AU  - Bouleau, Nicolas
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
UR  - https://www.numdam.org/articles/10.1016/j.crma.2008.05.020/
DO  - 10.1016/j.crma.2008.05.020
LA  - en
ID  - CRMATH_2008__346_13-14_779_0
ER  - 
%0 Journal Article
%A Bouleau, Nicolas
%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
%U https://www.numdam.org/articles/10.1016/j.crma.2008.05.020/
%R 10.1016/j.crma.2008.05.020
%G en
%F CRMATH_2008__346_13-14_779_0
Bouleau, Nicolas. 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://www.numdam.org/articles/10.1016/j.crma.2008.05.020/

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

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

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

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

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

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

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

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

Cited by Sources: