THE UNIFORM LOCAL ASYMPTOTICS OF THE OVERSHOOT OF A RANDOM WALK WITH HEAVY-TAILED INCREMENTS

被引：13

作者：

Chen, Guochun ^{[1
]}

Wang, Yuebao ^{[1
]}

Cheng, Fengyang ^{[1
]}

机构：

[1] Suzhou Univ, Dept Math, Suzhou 215006, Peoples R China

来源：

STOCHASTIC MODELS | 2009年 / 25卷 / 03期

基金：

美国国家科学基金会;

关键词：

Local subexponential classes; Overshoot; Random walk; Uniform local asymptotics; MOMENTS; RUIN; SUMS; PROBABILITIES; SUPREMUM; MAXIMUM;

D O I：

10.1080/15326340903088859

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：

The article obtains the uniform local asymptotics of the overshoot of a random walk with heavy-tailed increments. When the overshoot is in (x + y, x + y + T] for some 0 < T < infinity, we discuss the asymptotics for the cases of y >= f (x) for any positive function f (x) -> infinity as x -> infinity and y is an element of [0, N] for any 0 < N < infinity, respectively. Based on the stated results, we get a unified form of the local asymptotics of the overshoot of a random walk for the case y >= 0. The obtained results require certain uniform requirements for y.

引用

页码：508 / 521

页数：14

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