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A conditional approach to the anticipating Girsanov transformation
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  • Published: September 1993

A conditional approach to the anticipating Girsanov transformation

  • Rainer Buckdahn1 &
  • Hans Föllmer2 

Probability Theory and Related Fields volume 95, pages 311–330 (1993)Cite this article

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  • 4 Citations

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Summary

We study the law of a stochastic differential equation

$$d\xi _t = d\omega _t + k_1 (\xi ,\omega )dt$$

where the drift anticipates the future behavior of the Brownian path ω, for example the endpoint. We first investigate anticipation of the endpoint, using a conditional Girsanov transformation and methods of Malliavin calculus. A combination with results of Buckdahn [2] leads to new versions of the anticipating Girsanov transformation of Ramer and Kusuoka, and in particular to explicit formulas for the Carleman-Fredholm determinant.

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References

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Humboldt-Universität, Unter den Linden 6, O-1086, Berlin, Federal Republic of Germany

    Rainer Buckdahn

  2. Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse 6, W-5300, Bonn, Federal Republic of Germany

    Hans Föllmer

Authors
  1. Rainer Buckdahn
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  2. Hans Föllmer
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Buckdahn, R., Föllmer, H. A conditional approach to the anticipating Girsanov transformation. Probab. Th. Rel. Fields 95, 311–330 (1993). https://doi.org/10.1007/BF01192167

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  • Received: 11 March 1991

  • Revised: 15 September 1992

  • Issue Date: September 1993

  • DOI: https://doi.org/10.1007/BF01192167

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Mathematics Subject Classification

  • 60H07
  • 60H10
  • 60J65
  • 60J45
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