First passage of a Markov additive process and generalized Jordan chains

Bernardo D' Auria, J. Ivanovs, O. Kella, M.R.H. Mandjes

Research output: Contribution to journalArticleAcademicpeer-review

29 Citations (Scopus)

Abstract

In this paper we consider the first passage process of a spectrally negative Markov additive process (MAP). The law of this process is uniquely characterized by a certain matrix function, which plays a crucial role in fluctuation theory. We show how to identify this matrix using the theory of Jordan chains associated with analytic matrix functions. This result provides us with a technique that can be used to derive various further identities.
Original languageEnglish
Pages (from-to)1048-1057
JournalJournal of Applied Probability
Volume47
Issue number4
DOIs
Publication statusPublished - 2010

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