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Stochastic Analysis on Lie Groups

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Stochastic Analysis and Related Topics VI

Part of the book series: Progress in Probability ((PRPR,volume 42))

Abstract

In this article we begin by reviewing the recent results regarding the analysis constructed on the Lie group-valued paths and loops equipped with probability measures which correspond to the Lie-Stratonovitch exponentiation of the Brownian path in the corresponding Lie algebra. In the last section we give some new results about the quasi-invariance of the anticipative left-shifts and the associated degree theorem for the paths and based loops.

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Authors
  1. A. S. Üstünel
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Editor information

Editors and Affiliations

  1. Département Réseaux, École Nationale Supérieure des Télécommunications, 46, rue Barrault, 75634, Paris Cedex 13, France

    Laurent Decreusefond  & Ali Süleyman Üstünel  & 

  2. Dept. of Mathematics, University of Oslo, Box 1053 Blindern, N-0316, Oslo, Norway

    Bernt Øksendal

  3. Central Bureau of Statistics, Norwegian Computing Center, Box 8131 DEP, N-0316, Oslo, Norway

    Jon Gjerde

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© 1998 Springer Science+Business Media New York

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Üstünel, A.S. (1998). Stochastic Analysis on Lie Groups. In: Decreusefond, L., Øksendal, B., Gjerde, J., Üstünel, A.S. (eds) Stochastic Analysis and Related Topics VI. Progress in Probability, vol 42. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2022-0_3

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  • DOI: https://doi.org/10.1007/978-1-4612-2022-0_3

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7385-1

  • Online ISBN: 978-1-4612-2022-0

  • eBook Packages: Springer Book Archive

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