TY - JOUR

T1 - Singularities of the matrix exponent of a Markov additive process with one-sided jumps

AU - Ivanovs, J.

AU - Boxma, O.J.

AU - Mandjes, M.R.H.

PY - 2010

Y1 - 2010

N2 - We analyze the number of zeros of det(F(a)), where F(a) 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(a) 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 Cramér–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.

AB - We analyze the number of zeros of det(F(a)), where F(a) 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(a) 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 Cramér–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.

U2 - 10.1016/j.spa.2010.05.007

DO - 10.1016/j.spa.2010.05.007

M3 - Article

SN - 0304-4149

VL - 120

SP - 1776

EP - 1794

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 9

ER -