A link between Bougerol's identity and a formula due to Donati-Martin, Matsumoto and Yor

Matyas Barczy; Peter Kern

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arXiv · 1403.5785

A link between Bougerol's identity and a formula due to Donati-Martin, Matsumoto and Yor

Matyas Barczy·Peter Kern

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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 $\alpha$-Wiener bridges or scaled Wiener bridges, which in case $\alpha=0$ coincides with a Wiener process and for $\alpha=1$ is a version of the Wiener bridge.

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Matyas Barczy, Peter Kern. 2014-03-23. A link between Bougerol's identity and a formula due to Donati-Martin, Matsumoto and Yor. https://arxiv.org/abs/1403.5785

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