## The Annals of Probability

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

### Functionals of Brownian Meander and Brownian Excursion

Richard T. Durrett and Donald L. Iglehart

#### 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 in Project Euclid: 19 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aop/1176995896

**Digital Object Identifier**

doi:10.1214/aop/1176995896

**Mathematical Reviews number (MathSciNet)**

MR436354

**Zentralblatt MATH identifier**

0356.60035

**JSTOR**

links.jstor.org

**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. Ann. Probab. 5 (1977), no. 1, 130--135. doi:10.1214/aop/1176995896. http://projecteuclid.org/euclid.aop/1176995896.