The Annals of Probability

Weak Convergence to Brownian Meander and Brownian Excursion

Richard T. Durrett, Donald L. Iglehart, and Douglas R. Miller

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Abstract

We show that (i) Brownian motion conditioned to be positive is Brownian meander; (ii) tied-down Brownian meander is Brownian excursion; and (iii) Brownian bridge conditioned to be positive is Brownian excursion. Using these results we derive the distribution of the suprema of the meander and excursion.

Article information

Source
Ann. Probab. Volume 5, Number 1 (1977), 117-129.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176995895

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176995895

Mathematical Reviews number (MathSciNet)
MR436353

Zentralblatt MATH identifier
0356.60034

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60B10: Convergence of probability measures

Keywords
Brownian motion Brownian meander Brownian bridge Brownian excursion distribution of supremum weak convergence

Citation

Durrett, Richard T.; Iglehart, Donald L.; Miller, Douglas R. Weak Convergence to Brownian Meander and Brownian Excursion. Ann. Probab. 5 (1977), no. 1, 117--129. doi:10.1214/aop/1176995895. http://projecteuclid.org/euclid.aop/1176995895.


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