First passage of a Markov additive process and generalized Jordan chains
AbstractIn 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.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws103923.
Date of creation: Oct 2010
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Lévy processes; Fluctuation theory; Markov Additive Processes;
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- D’Auria, Bernardo & Kella, Offer, 2012. "Markov modulation of a two-sided reflected Brownian motion with application to fluid queues," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1566-1581.
- Ivanovs, Jevgenijs, 2013. "A note on killing with applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 29-34.
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