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The composition of Wiener functionals with non absolutely continuous Shifts
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  • Published: June 1994

The composition of Wiener functionals with non absolutely continuous Shifts

  • A. S. Üstünel1 &
  • M. Zakai2 

Probability Theory and Related Fields volume 98, pages 163–184 (1994)Cite this article

Summary

In this paper we study some classes of Wiener functionals whose elements can be composed with a non-linear, non-absolutely continous transformation of the form of perturbation of identity in the direction of Cameron-Martin space. We show that under certain conditions the image of the Wiener measure under the above transformation induces a generalized Wiener functional on certain Sobolev spaces generalizing the Radon-Nikodym relation to non absolutely continuous transformations. A series representation for the generalized Radon-Nikodym derivative is presented and conditional expectations of some generalized random variables are considered.

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Author information

Authors and Affiliations

  1. E.N.S.T., 46, rue Barrault, F-75634, Paris, France

    A. S. Üstünel

  2. Department of Electrical Engineering, Technion, 32000, Haifa, Israel

    M. Zakai

Authors
  1. A. S. Üstünel
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  2. M. Zakai
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Üstünel, A.S., Zakai, M. The composition of Wiener functionals with non absolutely continuous Shifts. Probab. Th. Rel. Fields 98, 163–184 (1994). https://doi.org/10.1007/BF01192512

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  • Received: 02 December 1992

  • Revised: 03 August 1993

  • Issue Date: June 1994

  • DOI: https://doi.org/10.1007/BF01192512

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Mathematics Subject Classifiation

  • 60H05
  • 60G15
  • 60G30
  • 46G05
  • 46G12
  • 58B10
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