An excursion approach to maxima of the Brownian bridge

被引：3

作者：

Perman, Mihael ^{[1
,2
]}

Wellner, Jon A. ^{[3
]}

机构：

[1] Fac Math & Phys, SI-1000 Ljubljana, Slovenia

[2] Univ Primorska, Fac Math Nat Sci & Informat Technol, SI-6000 Koper, Slovenia

[3] Univ Washington, Dept Stat, Seattle, WA 98195 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2014年 / 124卷 / 09期

基金：

美国国家科学基金会;

关键词：

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

D O I：

10.1016/j.spa.2014.04.008

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：3106 / 3120

页数：15