Limit laws for Brownian motion conditioned to reach a high level
type: Item
instance of: scholarly article
title: Limit laws for Brownian motion conditioned to reach a high level
zbMATH Open document ID: 0769.60075
DOI: 10.1016/0167-7152(93)90188-O
published in: Statistics \& Probability Letters
publication date: 1993-05-24T00:00:00Z
review text: A functional limit theorem is presented for the behaviour of Brownian motion conditioned to reach a high level during a fixed time interval. The asymptotic behaviour of the conditioned path as the level tends to infinity is expressed via a time reversal and suitable renormalisation of space and time. Some relations to Williams' path decomposition is pointed out.
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 178024
zbMATH Keywords: functional limit theorem
zbMATH Keywords: Brownian motion
zbMATH Keywords: asymptotic behaviour of the conditioned path
zbMATH Keywords: renormalisation of space and time
author: Michael J. Klass
author: Jim Pitman
reviewed by: Uwe Rösler
MaRDI profile type: Publication
cites work: Sojourns and extremes of a diffusion process on a fixed interval
cites work: Fluctuation identities for lévy processes and splitting at the maximum
cites work: Q5332526
cites work: A conditional limit law result on the location of the maximum of Brownian motion
cites work: Zero-One Laws and the Minimum of a Markov Process
cites work: Markov functions
cites work: It� excursion theory via resolvents
cites work: Path Decomposition and Continuity of Local Time for One-Dimensional Diffusions, I
full work available at URL: 0167-7152(93)90188-o
OpenAlex ID: W2050465394
description: scientific article; zbMATH DE number 178024