Brownian bridge on hyperbolic spaces and on homogeneous trees
type: Item
instance of: scholarly article
title: Brownian bridge on hyperbolic spaces and on homogeneous trees
zbMATH Open document ID: 0947.58032
author: Philippe Bougerol
author: Thierry Jeulin
publication date: 2000-10-23T00:00:00Z
review text: Consider the Brownian bridge \(B^{(\nu)}\) of length \(\nu\) on a noncompact non Euclidean rank one symmetric space \(H\) (for instance a hyperbolic space), and with origin a fixed point \(o\) of \(H\). Let \(R_t^{(\nu)} = d(o,B_t^{(\nu)})\). It is proved that \((R_{t\nu}^{(\nu)}/\sqrt\nu ; 0\leq t\leq 1)\) converges in distribution to the real-valued Brownian excursion. The same result is proved for homogeneous trees. The introduction of the article explains the motivations for this study; in particular, the order of magnitude which is obtained for the Brownian bridge in this result has important physical applications.
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 1371488
zbMATH Keywords: Brownian bridge
zbMATH Keywords: symmetric space
zbMATH Keywords: tree
zbMATH Keywords: excursion
zbMATH Keywords: hyperbolic space
reviewed by: Jean Picard
MaRDI profile type: Publication
full work available at URL: s004400050237
OpenAlex ID: W2071909162
DOI: 10.1007/S004400050237
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1371488