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
VL - 120
SP - 1776
EP - 1794
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 9
ER -