An excursion approach to maxima of the Brownian Bridge

Mihael Perman; Jon A. Wellner

doi:10.1016/j.spa.2014.04.008

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arXiv · 0904.3473

An excursion approach to maxima of the Brownian Bridge

Mihael Perman·Jon A. Wellner

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Abstract

Functionals of Brownian bridge arise as limiting distributions in nonparametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. Only the Poisson character of the excursion process will be used. Particular cases of calculations include the distributions of the Kolmogorov-Smirnov statistic, the Kuiper statistic, and the ratio of the maximum positive ordinate to the minumum negative ordinate.

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Mihael Perman, Jon A. Wellner. 2014-06-14. An excursion approach to maxima of the Brownian Bridge. https://doi.org/10.1016/j.spa.2014.04.008

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