Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 77-81 |
Journal | Operations Research Letters |
Volume | 38 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2010 |