The lifetime of conditioned Brownian motion in certain Lipschitz domains
type: Item
instance of: scholarly article
title: The lifetime of conditioned Brownian motion in certain Lipschitz domains
zbMATH Open document ID: 0592.60068
DOI: 10.1007/BF00320080
publication date: 1987-01-01T00:00:00Z
review text: For certain Lipschitz domains D we obtain a series expansion for the distribution of the lifetime \(\tau_ D\) of conditioned Brownian motion on D. From this we determine \[ \lim_{t\to \infty}t^{-1} \log P^ h_ x(\tau_ D>t)=\lim_{t\to \infty}t^{-1}\quad \log P_ x(\tau_ D>t)=-\lambda_ D, \] where \(\lambda_ D\) is the first eigenvalue of \(\Delta\) /2 on D.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 3951734
zbMATH Keywords: series expansion for the distribution of the lifetime
zbMATH Keywords: conditioned Brownian motion
zbMATH Keywords: first eigenvalue
author: Richard Dante DeBlassie
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 3951734