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First passage of a Markov additive process and generalized Jordan chains

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

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

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, which can be used to derive various further identities.

Keywords: Lévy; processes; Fluctuation; theory; Markov; Additive; Processes (search for similar items in EconPapers)
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Date: 2010-10
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