The Matsumoto and Yor process and infinite dimensional hyperbolic space

Philippe Bougerol (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: espace symétrique; Mouvement brownien

Domaines: Probabilités [math.PR]

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