The Annals of Probability

Functionals of Brownian Meander and Brownian Excursion

Richard T. Durrett and Donald L. Iglehart

Full-text: Open access

Abstract

The primary concern of this paper is to calculate the distributions and/or means of the maxima, first entrance times, and occupation times of Brownian meander and Brownian excursion. The method employed is to develop conditioned families of random functions which have Brownian meander (or Brownian excursion) as their weak limit and then use the continuous mapping theorem.

Article information

Source
Ann. Probab. Volume 5, Number 1 (1977), 130-135.

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176995896

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176995896

Mathematical Reviews number (MathSciNet)
MR436354

Zentralblatt MATH identifier
0356.60035

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60J65: Brownian motion [See also 58J65] 60F05: Central limit and other weak theorems

Keywords
Brownian excursion Brownian meander conditioned limit theorems functional central limit theorems maxima of processes occupation time density weak convergence

Citation

Durrett, Richard T.; Iglehart, Donald L. Functionals of Brownian Meander and Brownian Excursion. The Annals of Probability 5 (1977), no. 1, 130--135. doi:10.1214/aop/1176995896. http://projecteuclid.org/euclid.aop/1176995896.


Export citation