The maximum of Brownian motion with parabolic drift

被引：13

作者：

Janson, Svante ^{[1
]}

Louchard, Guy ^{[2
]}

Martin-Lof, Anders ^{[3
]}

机构：

[1] Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden

[2] Univ Libre Bruxelles, Dept Informat, B-1050 Brussels, Belgium

[3] Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2010年 / 15卷

关键词：

Brownian motion; parabolic drift; Airy functions; MEAN PATH; INTEGRALS; SIZE; TIME;

D O I：

10.1214/EJP.v15-830

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：

We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give new series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.

引用

页码：1893 / 1929

页数：37

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