TY - JOUR
T1 - First passage of time-reversible spectrally negative Markov additive processes
AU - Ivanovs, J.
AU - Mandjes, M.R.H.
PY - 2010
Y1 - 2010
N2 - We study the first passage process of a spectrally negative Markov additive process (MAP). The focus is on the background Markov chain at the times of the first passage. This process is a Markov chain itself with a transition rate matrix ¿. Assuming time reversibility, we show that all the eigenvalues of ¿ are real, with algebraic and geometric multiplicities being the same, which allows us to identify the Jordan normal form of ¿. Furthermore, this fact simplifies the analysis of fluctuations of a MAP. We provide an illustrative example and show that our findings greatly reduce the computational efforts required to obtain ¿ in the time-reversible case.
AB - We study the first passage process of a spectrally negative Markov additive process (MAP). The focus is on the background Markov chain at the times of the first passage. This process is a Markov chain itself with a transition rate matrix ¿. Assuming time reversibility, we show that all the eigenvalues of ¿ are real, with algebraic and geometric multiplicities being the same, which allows us to identify the Jordan normal form of ¿. Furthermore, this fact simplifies the analysis of fluctuations of a MAP. We provide an illustrative example and show that our findings greatly reduce the computational efforts required to obtain ¿ in the time-reversible case.
U2 - 10.1016/j.orl.2009.10.014
DO - 10.1016/j.orl.2009.10.014
M3 - Article
SN - 0167-6377
VL - 38
SP - 77
EP - 81
JO - Operations Research Letters
JF - Operations Research Letters
IS - 2
ER -