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Applications of the degree theorem to absolute continuity on Wiener space
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  • Published: December 1993

Applications of the degree theorem to absolute continuity on Wiener space

  • A. S. Üstünel1 &
  • M. Zakai2 

Probability Theory and Related Fields volume 95, pages 509–520 (1993)Cite this article

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  • 12 Citations

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Summary

Let (Ω,H, P) be an abstract Wiener space and define a shift on Ω byT(ω)=ω+F(ω) whereF is anH-valued random variable. We study the absolute continuity of the measuresPºT −1and (Λ F P)ºT ∔1 with respect toP using the techniques of the degree theory of Wiener maps, where Λ F =det2(1+▽F) × Exp{−δF−1/2|F|2}.

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Author information

Authors and Affiliations

  1. E.N.S.T., Départment Réseaux, 46, rue Barrault, F-75634, Paris Cedex 13, 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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Additional information

The work of the second author was supported by the fund for promotion of research at the Technion

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Üstünel, A.S., Zakai, M. Applications of the degree theorem to absolute continuity on Wiener space. Probab. Th. Rel. Fields 95, 509–520 (1993). https://doi.org/10.1007/BF01196731

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  • Received: 10 February 1992

  • Revised: 23 September 1992

  • Issue Date: December 1993

  • DOI: https://doi.org/10.1007/BF01196731

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Mathematics Subject Classification

  • 60G30
  • 60H07
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