An excursion approach to maxima of the Brownian bridge

作者：Perman Mihael^*; Wellner Jon A

来源：Stochastic Processes and Their Applications, 2014, 124(9): 3106-3120.

DOI：10.1016/j.spa.2014.04.008

• Brownian bridge
• Resealing
• Excursions
• Extrema
• Kolmogorov-Smirnov statistics

Distributions of functionals of Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. The idea of resealing and conditioning on the local time has been used widely in the literature. In this paper it is used to give a unified derivation of a number of known distributions, and a few new ones. Particular cases of calculations include the distribution of the Kolmogorov-Smimov statistic and the Kuiper statistic.

• 出版日期2014-9