Probability Theory and Related Fields

, Volume 95, Issue 4, pp 509–520

Applications of the degree theorem to absolute continuity on Wiener space

  • A. S. Üstünel
  • M. Zakai
Article

DOI: 10.1007/BF01196731

Cite this article as:
Üstünel, A.S. & Zakai, M. Probab. Th. Rel. Fields (1993) 95: 509. doi:10.1007/BF01196731

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 (ΛFPT∔1 with respect toP using the techniques of the degree theory of Wiener maps, where ΛF=det2(1+▽F) × Exp{−δF−1/2|F|2}.

Mathematics Subject Classification

60G30 60H07 

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • A. S. Üstünel
    • 1
  • M. Zakai
    • 2
  1. 1.E.N.S.T., Départment RéseauxParis Cedex 13France
  2. 2.Department of Electrical EngineeringTechnionHaifaIsrael

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