## Electronic Journal of Probability

### Tail estimates for the Brownian excursion area and other Brownian areas

#### Abstract

Brownian areas are considered in this paper: the Brownian excursion area, the Brownian bridge area, the Brownian motion area, the Brownian meander area, the Brownian double meander area, the positive part of Brownian bridge area, the positive part of Brownian motion area. We are interested in the asymptotics of the right tail of their density function. Inverting a double Laplace transform, we can derive, in a mechanical way, all terms of an asymptotic expansion. We illustrate our technique with the computation of the first four terms. We also obtain asymptotics for the right tail of the distribution function and for the moments. Our main tool is the two-dimensional saddle point method.

#### Article information

Source
Electron. J. Probab., Volume 12 (2007), paper no. 58, 1600-1632.

Dates
Accepted: 23 December 2007
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464818529

Digital Object Identifier
doi:10.1214/EJP.v12-471

Mathematical Reviews number (MathSciNet)
MR2365879

Zentralblatt MATH identifier
1189.60148

Subjects
Primary: AMS 2000 Subject Classification: 60J65

Rights

#### Citation

Janson, Svante; Louchard, Guy. Tail estimates for the Brownian excursion area and other Brownian areas. Electron. J. Probab. 12 (2007), paper no. 58, 1600--1632. doi:10.1214/EJP.v12-471. https://projecteuclid.org/euclid.ejp/1464818529

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