Singularities of the matrix exponent of a Markov additive process with one-sided jumps

被引：17

作者：

Ivanovs, Jevgenijs ^{[1
,3
]}

Boxma, Onno ^{[1
,2
]}

Mandjes, Michel ^{[1
,3
]}

机构：

[1] Eindhoven Univ Technol, EURANDOM, NL-5600 MB Eindhoven, Netherlands

[2] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

[3] Univ Amsterdam, Korteweg de Vries Inst Math, NL-1098 XH Amsterdam, Netherlands

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2010年 / 120卷 / 09期

关键词：

Markov additive processes; Levy processes; Queueing theory; Markov modulation; First passage; Roots of Cramer-Lundberg equation; Argument principle; FLUID MODELS; QUEUE;

D O I：

10.1016/j.spa.2010.05.007

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 analyze the number of zeros of det(F(alpha)), where F(alpha) is the matrix exponent of a Markov Additive Process (MAP) with one-sided jumps. The focus is on the number of zeros in the right half of the complex plane, where F(alpha) is analytic. In addition, we also consider the case of a MAP killed at an independent exponential time. The corresponding zeros can be seen as the roots of a generalized Cramer-Lundberg equation. We argue that our results are particularly useful in fluctuation theory for MAPs, which leads to numerous applications in queueing theory and finance. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1776 / 1794

页数：19

共 26 条

[1] On the application of Rouche's theorem in queueing theory [J].