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 uctuations 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 |
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Place of Publication | Eindhoven |
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Publisher | Eurandom |
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Number of pages | 8 |
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Publication status | Published - 2009 |
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Name | Report Eurandom |
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Volume | 2009048 |
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ISSN (Print) | 1389-2355 |
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