Distributions of the longest excursions in a tied down simple random walk and in a Brownian bridge

被引：2

作者：

Lindell, Andreas ^{[1
]}

Holst, Lars ^{[1
]}

机构：

[1] Royal Inst Technol, Dept Math, SE-10044 Stockholm, Sweden

来源：

JOURNAL OF APPLIED PROBABILITY | 2007年 / 44卷 / 04期

关键词：

tied down random walk; Brownian bridge; ranked excursion length; weak convergence; generating function; Kummer function;

D O I：

10.1239/jap/1197908824

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：

Expressions for the joint distribution of the longest and second longest excursions as well as the marginal distributions of the three longest excursions in the Brownian bridge are obtained. The method, which primarily makes use of the weak convergence of the random walk to the Brownian motion, principally gives the possibility to obtain any desired joint or marginal distribution. Numerical illustrations of the results are also given.

引用

页码：1056 / 1067

页数：12

共 7 条

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