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On Striking Identities About the Exponential Functionals of the Brownian Bridge and Brownian Motion

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Abstract

The negative moment of order 1, resp. of order 1/2, for the integral on (0, 1) of the exponential of α times the Brownian bridge, resp. the Brownian motion, does not depend on α. We give a simple explanation and a reinforcement of this property in the case of the Brownian bridge. We then discuss how different the case of the Brownian motion is.

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Authors and Affiliations

  1. Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex 04, France

    Catherine Donati-Martin

  2. School of Informatics and Sciences, Nagoya University Chikusa-ku, Nagoya, 464-8601, Japan

    Hiroyuki Matsumoto

  3. Laboratoire de Probabilités, Université Pierre et Marie Curie, 4, Place Jussieu, Tour 56, F-75252, Paris Cedex 05, France

    Marc Yor

Authors
  1. Catherine Donati-Martin
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  2. Hiroyuki Matsumoto
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  3. Marc Yor
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Donati-Martin, C., Matsumoto, H. & Yor, M. On Striking Identities About the Exponential Functionals of the Brownian Bridge and Brownian Motion. Periodica Mathematica Hungarica 41, 103–119 (2000). https://doi.org/10.1023/A:1010308203346

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