Branching properties of Brownian paths and trees
type: Item
instance of: scholarly article
title: Branching properties of Brownian paths and trees
zbMATH Open document ID: 0901.60051
author: Romain Abraham
author: Laurent Mazliak
published in: Expositiones Mathematicae
publication date: 1998-11-11T00:00:00Z
review text: The authors present the construction of an infinite tree structure associated to a Brownian excursion. The construction is inspired by the results of \textit{J.-F. Le Gall} [in: Séminaire de probabilités XXIII, Lect. Notes Math. 1372, 258-274 (1989; Zbl 0741.60078)], \textit{J. Neveu} and \textit{J.W. Pitman} [ibid., 248-257 (1989; Zbl 0741.60081)], \textit{J.-F. Le Gall} [Ann. Probab. 19, No. 4, 1399-1439 (1991; Zbl 0753.60078)] and \textit{R. Abraham} [in: Séminaire de probabilités XXVI, Lect. Notes Math. 1526, 374-397 (1992; Zbl 0763.60035)]. The same work is done for a reflected Brownian motion perturbed by its local time. These constructions are used to derive an alternative proof of the generalized Ray-Knight theorem.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 1151669
zbMATH Keywords: Brownian excursion
zbMATH Keywords: branching process
zbMATH Keywords: reflected Brownian motion
zbMATH Keywords: local time
reviewed by: Mihai Gradinaru
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1151669