Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1142596 | Operations Research Letters | 2010 | 5 Pages |
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 Î. Assuming time reversibility, we show that all the eigenvalues of Î are real, with algebraic and geometric multiplicities being the same, which allows us to identify the Jordan normal form of Î. 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 Î in the time-reversible case.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jevgenijs Ivanovs, Michel Mandjes,