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Transformation of Wiener measure under anticipative flows
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  • Published: March 1992

Transformation of Wiener measure under anticipative flows

  • Ali Süleyman Üstünel1 &
  • Moshe Zakai2 

Probability Theory and Related Fields volume 93, pages 91–136 (1992)Cite this article

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Summary

LetT(ω)=ω+F(ω) be a transformation from the Wiener space to itself with the range ofF(ω) assumed to be in the Cameron-Martin space. The absolute continuity and the density function associated withT is considered;T is assumed to be embedded in or defined through a parameterizationT t ω=ω+F t (ω) andF t is assumed to be differentiable int. The paper deals first with the case where the range of thet-derivative ofF t (ω) is also in the Cameron-Martin space and new representations for the Radon-Nikodym derivative and the Carleman-Fredholm determinant are derived. The case where thet-derivative ofF t is not in the Cameron-Martin space is considered next and results on the absolute continuity and the density function, under conditions which are considerably weaker than previously known conditions, are presented.

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Author information

Authors and Affiliations

  1. Département Réseaux, E.N.S.T., 46, rue Barrault, F-75634, Paris Cedex 13, France

    Ali Süleyman Üstünel

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

    Moshe Zakai

Authors
  1. Ali Süleyman Üstünel
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  2. Moshe 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. Transformation of Wiener measure under anticipative flows. Probab. Th. Rel. Fields 93, 91–136 (1992). https://doi.org/10.1007/BF01195390

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  • Received: 03 July 1991

  • Revised: 02 January 1992

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01195390

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Keywords

  • Density Function
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Absolute Continuity
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