Tail estimates for the Brownian excursion area and other Brownian areas
Svante Janson, Uppsala University
Guy Louchard, ULB
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.
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