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The Annals of Probability
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Weak Convergence to Brownian Excursion

Weak convergence to Brownian excursion
descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Aug 1983Publisher:Institute of Mathematical StatisticsJournal:The Annals of Probability, volume 11 (issn: 0091-1798, Copyright policy )
Authors: Blumenthal, R. M.;

doi: 10.1214/aop/1176993525

Weak Convergence to Brownian Excursion

Abstract

We give a concise proof, using rescaling, random time change and simple infinitesimal generator computations of the fact that Brownian excursion is the weak limit as $\varepsilon \rightarrow 0$ of tied down Brownian motion conditioned never to fall below $-\varepsilon$.

Keywords

60B10, infinitesimal generator, Brownian excursion, Bessel process, Transition functions, generators and resolvents, 60J65, Brownian motion, Convergence of probability measures, random time change

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Average
Top 10%
Average
Green
hybrid