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Tail estimates for the Brownian excursion area and other Brownian areas
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 12, 1600-1632 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2007. Vol. 12, 1600-1632 p.
Keyword [en]
Brownian areas, asymptotics for density functions right tail, double Laplace transform, two-dimensional saddle point method
National Category
URN: urn:nbn:se:uu:diva-12753ISI: 000251967100002OAI: oai:DiVA.org:uu-12753DiVA: diva2:40522
Available from: 2008-01-11 Created: 2008-01-11 Last updated: 2010-05-18Bibliographically approved

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Janson, Svante
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