Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Brownian bridge on Riemannian symmetric spaces

Auteur(s):

Code(s) de Classification MSC:

• 43A85 Analysis on homogeneous spaces
Résumé: We consider the Brownian bridge of length $T$ on a symmetric space of the non compact type. We prove that this process, after a scaling, converges when $T \to +\infty‚$ to a process the generalized radial part of which is the bridge of the Euclidean Brownian motion in the Weyl chamber killed at the boundary.