First passage of time-reversible spectrally negative Markov additive processes

First passage of time-reversible spectrally negative Markov additive processes

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Article ID: iaor20101725
Volume: 38
Issue: 2
Start Page Number: 77
End Page Number: 81
Publication Date: Mar 2010
Journal: Operations Research Letters
Authors: ,
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 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.

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