First passage of a Markov additive process and generalized Jordan chains

Bernardo D'Auria*, Jevgenijs Ivanovs, Offer Kella, Michel Mandjes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

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 languageAmerican English
Pages (from-to)1048-1057
Number of pages10
JournalJournal of Applied Probability
Volume47
Issue number4
DOIs
StatePublished - Dec 2010

Keywords

  • Fluctuation theory
  • Lévy process
  • Markov additive process

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