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The Matsumoto and Yor process and infinite dimensional hyperbolic space

Abstract : The Matsumoto\,--Yor process is $\int_0^t \exp(2B_s-B_t)\, ds$, where $(B_t)$ is a Brownian motion. It is shown that it is the limit of the radial part of the Brownian motion at the bottom of the spectrum on the hyperbolic space of dimension $q$, when $q$ tends to infinity. Analogous processes on infinite series of non compact symmetric spaces and on regular trees are described.
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https://hal.archives-ouvertes.fr/hal-01053806
Contributor : Philippe Bougerol <>
Submitted on : Friday, February 6, 2015 - 4:12:55 PM
Last modification on : Friday, March 27, 2020 - 3:07:32 AM
Document(s) archivé(s) le : Thursday, May 7, 2015 - 10:06:27 AM

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  • HAL Id : hal-01053806, version 2
  • ARXIV : 1408.2108

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Philippe Bougerol. The Matsumoto and Yor process and infinite dimensional hyperbolic space. 2014. ⟨hal-01053806v2⟩

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