Application of the lent particle method to Poisson-driven SDEs
نویسندگان
چکیده
منابع مشابه
Application of the lent particle method to Poisson driven SDE's
We apply the Dirichlet forms version of Malliavin calculus to stochastic differential equations with jumps. As in the continuous case this weakens significantly the assumptions on the coefficients of the SDE. In spite of the use of the Dirichlet forms theory, this approach brings also an important simplification which was not available nor visible previously : an explicit formula giving the car...
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We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for the laws of random functionals of Lévy processes or solutions of stochastic differential equations with jumps. As in the Wiener case the Dirichlet form approach weakens significantly the regularity assumptions. The main nove...
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In previous works ([11, 12]) we have introduced a new method called the lent particle method which is an efficient tool to establish existence of densities for Poisson functionals. We now go further and iterate this method in order to prove smoothness of densities. More precisely, we construct Sobolev spaces of any order and prove a Malliavin-type criterion of existence of smooth density. We ap...
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We propose a new method to apply the Lipschitz functional calculus of local Dirichlet forms to Poisson random measures. Résumé Calcul d’erreur et régularité des fonctionnelles de Poisson : la méthode de la particule prêtée. Nous proposons une nouvelle méthode pour appliquer le calcul fonctionnel lipschitzien des formes de Dirichlet locales aux mesures aléatoires de Poisson. 1 Notation and basic...
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We introduce a new approach to absolute continuity of laws of Poisson functionals. It is based on the energy image density property for Dirichlet forms. The associated gradient is a local operator and gives rise to a nice formula called the lent particle method which consists in adding a particle and taking it back after some calculation. AMS 2000 subject classifications: Primary 60G57, 60H05 ;...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2010
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-010-0303-x