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First passage of a Markov additive process and generalized Jordan chains

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Author Info

  • Bernardo D'Auria

    ()

  • Offer Kella,

    ()

  • Jevgenijs Ivanovs

    ()

  • Michel Mandjes

    ()

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    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.

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    File URL: http://e-archivo.uc3m.es/bitstream/10016/9362/1/ws103923.pdf
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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws103923.

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    Date of creation: Oct 2010
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    Handle: RePEc:cte:wsrepe:ws103923

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    Related research

    Keywords: Lévy processes; Fluctuation theory; Markov Additive Processes;

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    Cited by:
    1. 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.
    2. Ivanovs, Jevgenijs, 2013. "A note on killing with applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 29-34.
    3. Li, Shuanming & Ren, Jiandong, 2013. "The maximum severity of ruin in a perturbed risk process with Markovian arrivals," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 993-998.
    4. Hansjörg Albrecher & Jevgenijs Ivanovs, 2013. "A Risk Model with an Observer in a Markov Environment," Risks, MDPI, Open Access Journal, vol. 1(3), pages 148-161, November.

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