# 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01053806
Contributor : Philippe Bougerol <>
Submitted on : Friday, August 1, 2014 - 6:49:18 PM
Last modification on : Thursday, March 26, 2020 - 9:14:34 PM
Document(s) archivé(s) le : Tuesday, November 25, 2014 - 11:26:33 PM

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### Identifiers

• HAL Id : hal-01053806, version 1
• ARXIV : 1408.2108

### Citation

Philippe Bougerol. The Matsumoto and Yor process and infinite dimensional hyperbolic space. 2014. ⟨hal-01053806v1⟩

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