First passage of a Markov additive process and generalized Jordan chains

Bernardo D'Auria; Jevgenijs Ivanovs; Offer Kella; Michel Mandjes

doi:10.1239/jap/1294170518

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

Department of Statistics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1048-1057
Number of pages	10
Journal	Journal of Applied Probability
Volume	47
Issue number	4
DOIs	https://doi.org/10.1239/jap/1294170518
State	Published - Dec 2010

Keywords

Fluctuation theory
Lévy process
Markov additive process

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10.1239/jap/1294170518

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AU - Mandjes, Michel

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AB - 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.

KW - Fluctuation theory

KW - Lévy process

KW - Markov additive process

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First passage of a Markov additive process and generalized Jordan chains

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Keywords

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