A renewal theorem and supremum of a perturbed random walk

被引：0
|
作者：
Damek, Ewa [1 ]
Kolodziejek, Bartosz [2 ]
机构：
[1] Wroclaw Univ, Wroclaw, Poland
[2] Warsaw Univ Technol, Warsaw, Poland
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2018年 / 23卷
关键词：
perturbed random walk; regular variation; renewal theory; DIVERGENT PERPETUITIES; RUIN PROBABILITIES; TAIL ASYMPTOTICS; LIMIT-THEOREMS; MAXIMUM;
D O I：
10.1214/18-ECP184
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 tails of the supremum of a perturbed random walk under regime which was not yet considered in the literature. Our approach is based on a new renewal theorem, which is of independent interest. We obtain first and second order asymptotics of the solution to renewal equation under weak assumptions and we apply these results to obtain first and second order asymptotics of the tail of the supremum of a perturbed random walk.
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页数：13
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