2011-12-01, English, Article, Report edition: Application of the lent particle method to Poisson-driven SDEs.(Report) Bouleau, Nicolas; Denis, Laurent

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Physical Description
  • Report
  • Magazine/​Journal article
Published
  • Springer, 2011 Dec
Language
  • English

Edition details

Title
  • Application of the lent particle method to Poisson-driven SDEs.(Report)
Also Titled
  • Application of the lent particle method to Poisson-driven SDEs.
Appears In
  • Probability Theory and Related Fields, v.151, no.3-4, 2011 Dec, p.403(31) (ISSN: 0178-8051)
Author
  • Bouleau, Nicolas
  • Denis, Laurent
Published
  • Springer, 2011 Dec
Physical Description
  • Report
  • Magazine/​Journal article
Subjects
Target Audience
  • Academic
Summary
  • Byline: Nicolas Bouleau (1), Laurent Denis (2) Keywords: Stochastic differential equation; Poisson functional; Dirichlet form; Energy image density; Levy processes; Gradient; Carre du champ; Primary 60G57; 60H05; Secondary 60J45; 60G51 Abstract: We apply the Dirichlet form theory to stochastic differential equations with jumps as extension of Malliavin calculus reasoning. As in the continuous case, this weakens significantly the assumptions on the coefficients of the SDE. Thanks to the flexibility of the Dirichlet forms language, this approach brings also an important simplification which was neither available nor visible previously: an explicit formula giving the carre du champ matrix, i.e., the Malliavin matrix. Following this formula a new procedure appears, called the lent particle method which shortens the computations both theoretically and in concrete examples. In this paper which uses the construction done in Bouleau and Denis (J. Funct. Analysis 257:1144--1174, 2009) we restrict ourselves to the existence of densities smoothness will be studied separately. Author Affiliation: (1) Ecole des Ponts, Paris Tech, Paris-Est, 6 Avenue Blaise Pascal, 77455, Marne-La-Vallee Cedex 2, France (2) Equipe Analyse et Probabilites, Universite d'Evry-Val-d'Essonne, Boulevard Francois Mitterrand, 91025, Evry Cedex, France Article History: Registration Date: 03/​05/​2010 Received Date: 13/​04/​2009 Online Date: 23/​06/​2010
Terms of Use
  • COPYRIGHT 2011 Springer
Language
  • English
Database
  • Gale Academic OneFile
Identifier
  • 271600658

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