On subexponential tails for the maxima of negatively driven compound renewal and Levy processes

被引：4

作者：

Korshunov, Dmitry ^{[1
]}

机构：

[1] Univ Lancaster, Lancaster, England

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2018年 / 128卷 / 04期

关键词：

Levy process; Compound renewal process; Distribution tails; Heavy tails; Long-tailed distributions; Subexponential distributions; Random walk; PROBABILITIES; ASYMPTOTICS; SUPREMUM; TIME;

D O I：

10.1016/j.spa.2017.07.013

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 subexponential tail asymptotics for the distribution of the maximum M-t := suP(u is an element of[0,t]) X-u of a process X-t with negative drift for the entire range of t > 0. We consider compound renewal processes with linear drift and Levy processes. For both processes we also formulate and prove the principle of a single big jump for their maxima. The class of compound renewal processes with drift particularly includes the Cramer-Lundberg renewal risk process. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：1316 / 1332

页数：17

共 24 条

[1]

[Anonymous], 2003, Applied probability and queues

[2]

[Anonymous], 2013, Cambridge Studies in Advanced Mathematics

[3] Large deviations results for subexponential tails, with applications to insurance risk [J].