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Integration by parts formula and applications to equations with jumps
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  • Published: 30 June 2010

Integration by parts formula and applications to equations with jumps

  • Vlad Bally1 &
  • Emmanuelle Clément1 

Probability Theory and Related Fields volume 151, pages 613–657 (2011)Cite this article

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  • 26 Citations

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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.

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Authors and Affiliations

  1. Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris-Est, UMR 8050, 5 Bld Descartes, Champs-sur-marne, 77454, Marne-la-Vallée Cedex 2, France

    Vlad Bally & Emmanuelle Clément

Authors
  1. Vlad Bally
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  2. Emmanuelle Clément
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Correspondence to Vlad Bally.

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Cite this article

Bally, V., Clément, E. Integration by parts formula and applications to equations with jumps. Probab. Theory Relat. Fields 151, 613–657 (2011). https://doi.org/10.1007/s00440-010-0310-y

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  • Received: 13 November 2009

  • Revised: 02 June 2010

  • Published: 30 June 2010

  • Issue Date: December 2011

  • DOI: https://doi.org/10.1007/s00440-010-0310-y

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Keywords

  • Integration by parts formula
  • Malliavin calculus
  • Stochastic equations
  • Poisson point measures

Mathematics Subject Classification (2000)

  • Primary 60H07
  • Secondary 60G51
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