Boundary Crossing Problems for Compound Renewal Processes

被引：0

作者：

Borovkov, A. A. ^{[1
]}

机构：

[1] Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2020年 / 61卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

compound renewal process; boundary crossing problems; large deviation; ruin probability problem; RANDOM-WALK; LIMIT-THEOREMS; NEGATIVE DRIFT; MAXIMUM; ASYMPTOTICS;

D O I：

10.1134/S0037446620010036

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find sharp asymptotics of the probability that the trajectory of a compound renewal process crosses (or does not cross) an arbitrary remote boundary. In particular, some limit theorems are obtained for the distribution of the maximum of the process in the domain of large deviations. We also give some applications to the classical ruin probability problem in insurance theory.

引用

页码：21 / 46

页数：26

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