Ukrainian Mathematical Journal

, Volume 53, Issue 1, pp 134–140 | Cite as

Higher-Order Relations for Derivatives of Nonlinear Diffusion Semigroups

  • A. Val. Antonyuk
  • A. Vik. Antonyuk


We show that a special choice of the Cameron–Martin direction in the characterization of the Wiener measure via the formula of integration by parts leads to a set of natural representations for derivatives of nonlinear diffusion semigroups. In particular, we obtain a final solution of the non-Lipschitz singularities in the Malliavin calculus.


Final Solution Special Choice Nonlinear Diffusion Natural Representation Wiener Measure 
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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • A. Val. Antonyuk
    • 1
  • A. Vik. Antonyuk
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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