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2007 Tail estimates for the Brownian excursion area and other Brownian areas
Svante Janson, Guy Louchard
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Electron. J. Probab. 12: 1600-1632 (2007). DOI: 10.1214/EJP.v12-471


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.


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Svante Janson. Guy Louchard. "Tail estimates for the Brownian excursion area and other Brownian areas." Electron. J. Probab. 12 1600 - 1632, 2007.


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

zbMATH: 1189.60148
MathSciNet: MR2365879
Digital Object Identifier: 10.1214/EJP.v12-471

Primary: AMS 2000 Subject Classification: 60J65

Keywords: asymptotics for density functions right tail , Brownian areas , double Laplace transform , two-dimensional saddle point method

Vol.12 • 2007
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