First passage of a Markov additive process and generalized Jordan chains

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

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: Fluctuation; theory; Lévy; processes; Markov; Additive; Processes (search for similar items in EconPapers)
Date: 2010-10
New Economics Papers: this item is included in nep-ore
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Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:ws103923

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