Un théorème de Ray-Knight lié au supremum des temps locaux browniens. (A Ray-Knight theorem related to suprema of Brownian local times)
type: Item
instance of: scholarly article
title: Un théorème de Ray-Knight lié au supremum des temps locaux browniens. (A Ray-Knight theorem related to suprema of Brownian local times)
zbMATH Open document ID: 0688.60060
DOI: 10.1007/BF01217747
publication date: 1990-01-01T00:00:00Z
review text: Let \(\alpha\) denote the first hitting time of 1 by the supremum over nonnegative values of the space variable of the Brownian local times. We give a complete description in terms of Bessel processes for the law of the process (in the space variable) of the Brownian local times at time \(\alpha\). The proofs rely on stochastic calculus, excursion theory and especially the Ray-Knight theorems on Brownian local times. This result is applied to give a different proof of Borodin's result concerning the law of the supremum of Brownian local times taken at an independent exponential time.
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 4128194
zbMATH Keywords: first hitting time
zbMATH Keywords: local times
zbMATH Keywords: Bessel processes
zbMATH Keywords: Ray-Knight theorems on Brownian local times
author: Nathalie Eisenbaum
MaRDI profile type: Publication
cites work: Q3797994
cites work: Q3756256
cites work: Q3952948
cites work: On the joint distribution of the maximum and its location for a linear diffusion
cites work: Q3675284
cites work: A decomposition of the Brownian path
cites work: Random Walks and A Sojourn Density Process of Brownian Motion
cites work: A decomposition of Bessel Bridges
cites work: Asymptotic laws of planar Brownian motion
cites work: Sojourn times of diffusion processes
cites work: Path Decomposition and Continuity of Local Time for One-Dimensional Diffusions, I
cites work: Markov properties of Brownian local time
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4128194