The upper limit of a normalized random walk

被引：0

作者：

Zhang, Cun-Hui ^{[1
]}

机构：

[1] Rutgers State Univ, Dept Stat, Piscataway, NJ 08854 USA

来源：

Random Walk, Sequential Analysis and Related Topics: A FESTSCHRIFT IN HONOR OF YUAN-SHIH CHOW | 2006年

关键词：

random walk; strong law of large numbers; asymmetric random variables; integral test; law of the iterated logarithm; ladder variables; truncated moment;

D O I：

10.1142/9789812772558_0011

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 consider the upper limit of S-n/n(1/p) where S-n are partial sums of iid random variables. Under the assumption of E(X+)(P) < infinity, we provide an integral test which determines the upper limit up to certain universal constant factors depending on p only. The problem is closely related to moment properties of ladder variables. We prove our theorem by considering the lower limit of T-k/k(p) where Tk is the k-th epoch of the random walk.

引用

页码：157 / 167

页数：11

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