Ukrainian Mathematical Journal

, Volume 54, Issue 2, pp 266–279 | Cite as

Malliavin Calculus for Functionals with Generalized Derivatives and Some Applications to Stable Processes

  • A. M. Kulik


We introduce the notion of a generalized derivative of a functional on a probability space with respect to some formal differentiation. We establish a sufficient condition for the existence of the distribution density of a functional in terms of its generalized derivative. This result is used for the proof of the smoothness of the distribution of the local time of a stable process.


Distribution Density Formal Differentiation Local Time Probability Space Stable Process 
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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A. M. Kulik
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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