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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Ivanovs, Jevgenijs^1,3  Boxma, Onno^1,2  Mandjes, Michel^1,3 

[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

关键词: Markov additive processes;    Levy processes;    Queueing theory;    Markov modulation;    First passage;    Roots of Cramer-Lundberg equation;    Argument principle;   

DOI  :  10.1016/j.spa.2010.05.007

来源: Elsevier

【 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.

【 授权许可】

Free