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Probability Theory and Related Fields

, Volume 151, Issue 3–4, pp 613–657 | Cite as

Integration by parts formula and applications to equations with jumps

  • Vlad BallyEmail author
  • Emmanuelle Clément
Article

Abstract

We establish an integration by parts formula in an abstract framework in order to study the regularity of the law for processes arising as the solution of stochastic differential equations with jumps, including equations with discontinuous coefficients for which the Malliavin calculus developed by Bichteler et al. (Stochastics Monographs, vol 2. Gordon & Breach, New York, 1987) and Bismut (Z Wahrsch Verw Gebiete 63(2):147–235, 1983) fails.

Keywords

Integration by parts formula Malliavin calculus Stochastic equations Poisson point measures 

Mathematics Subject Classification (2000)

Primary 60H07 Secondary 60G51 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris-Est, UMR 8050Marne-la-Vallée Cedex 2France

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