Article ID: | iaor20101725 |
Volume: | 38 |
Issue: | 2 |
Start Page Number: | 77 |
End Page Number: | 81 |
Publication Date: | Mar 2010 |
Journal: | Operations Research Letters |
Authors: | Mandjes Michel, Ivanovs Jevgenijs |
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 Λ. Assuming time reversibility, we show that all the eigenvalues of Λ are real, with algebraic and geometric multiplicities being the same, which allows us to identify the Jordan normal form of Λ. 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 Λ in the time-reversible case.