First passage of time-reversible spectrally negative Markov additive processes

J. Ivanovs, M.R.H. Mandjes

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

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 languageEnglish
Pages (from-to)77-81
JournalOperations Research Letters
Volume38
Issue number2
DOIs
Publication statusPublished - 2010

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