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arXiv · 1408.2108

The Matsumoto and Yor process and infinite dimensional hyperbolic space

Philippe Bougerol
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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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Philippe Bougerol. 2014-08-09. The Matsumoto and Yor process and infinite dimensional hyperbolic space. https://arxiv.org/abs/1408.2108

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