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]
Comptes Rendus. Mathématique, Tome 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
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
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Bouleau, Nicolas. Error calculus and regularity of Poisson functionals: the lent particle method. Comptes Rendus. Mathématique, Tome 346 (2008) no. 13-14, pp. 779-782. doi : 10.1016/j.crma.2008.05.020. http://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

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