THE INTEGRAL OF THE SUPREMUM PROCESS OF BROWNIAN MOTION

被引：3
|
作者：
Janson, Svante [1 ]
Petersson, Niclas [1 ]
机构：
[1] Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden
来源：
JOURNAL OF APPLIED PROBABILITY | 2009年 / 46卷 / 02期
关键词：
Brownian motion; supremum process; local time; Brownian areas;
D O I：
10.1239/jap/1245676109
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：
In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area) A(T) covered by the process in the time interval [0, T]. The Laplace transform of A(T) follows as a consequence. The main proof involves a double Laplace transform of A(T) and is based on excursion theory and local time for Brownian motion.
引用
收藏
页码：593 / 600
页数：8
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