Asymptotics of the distribution of the integral of the positive part of the Brownian bridge for large arguments☆

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Abstract

The double Laplace transform of the distribution function of the integral of the positive part of the Brownian bridge was determined by M. Perman and J.A. Wellner, as well as the moments of this distribution. The purpose of the present paper is to determine the asymptotics of this distribution for large values of the argument, and the corresponding asymptotics of the moments.

Keywords

Distribution
Moments
Asymptotics
Brownian bridge
Airy functions
Saddle point

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This work was partly supported by the UK-EPSRC Grant GR/R71719/01.

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