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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References in corpus (2)

• Littelmann path model for geometric crystals, Whittaker functions on Lie groups and Brownian motion
• Matrix Dufresne Identity

Cited by in corpus (1)

• Matrix Dufresne Identity