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August, 1983 Weak Convergence to Brownian Excursion
R. M. Blumenthal
Ann. Probab. 11(3): 798-800 (August, 1983). DOI: 10.1214/aop/1176993525


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 $-\varepsilon$.


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R. M. Blumenthal. "Weak Convergence to Brownian Excursion." Ann. Probab. 11 (3) 798 - 800, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0515.60081
MathSciNet: MR704566
Digital Object Identifier: 10.1214/aop/1176993525

Primary: 60J65
Secondary: 60B10

Keywords: Bessel process , Brownian excursion , infinitesimal generator , Random time change

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 3 • August, 1983
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