An iterative approximation procedure for the distribution of the maximum of a random walk

被引：3

作者：

Stadje, W ^{[1
]}

机构：

[1] Univ Osnabruck, Fachbereich Math Informat, D-49069 Osnabruck, Germany

来源：

STATISTICS & PROBABILITY LETTERS | 2000年 / 50卷 / 04期

关键词：

random walk; maximum; approximation; embedded random walk;

D O I：

10.1016/S0167-7152(00)00124-3

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：

Let I(F) be the distribution function (d.f.) of the maximum of a random walk whose i.i.d. increments have the common d.f. F and a negative mean. We derive a recursive sequence of embedded random walks whose underlying d.f.'s Fk converge to the d.f. of the first ladder variable and satisfy F greater than or equal to F-1 greater than or equal to F-2 greater than or equal to ... on [0, infinity) and I(F) = I(F-1) = I(F-2) = .... Using these random walks we obtain improved upper bounds for the difference of I(F) and the d.f of the maximum of the random walk after finitely many steps. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：375 / 381

页数：7