Abstract
We point out an easy link between two striking identities on exponential functionals of the Wiener process and the Wiener bridge originated by Bougerol, and Donati-Martin, Matsumoto and Yor, respectively. The link is established using a continuous one-parameter family of Gaussian processes known as α-Wiener bridges or scaled Wiener bridges, which in case α = 0 coincides with a Wiener process and for α = 1 is a version of the Wiener bridge.
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Dedicated to the memory of Marc Yor 1949–2014
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Barczy, M., Kern, P. (2016). A Link Between Bougerol’s Identity and a Formula Due to Donati-Martin, Matsumoto and Yor. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLVIII. Lecture Notes in Mathematics(), vol 2168. Springer, Cham. https://doi.org/10.1007/978-3-319-44465-9_6
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DOI: https://doi.org/10.1007/978-3-319-44465-9_6
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