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Purely Excessive Functions and Hitting Times of Continuous-Time Branching Processes

Author

Listed:
  • F. Avram

    (Université de Pau et des Pays de l’Adour)

  • P. Patie

    (Cornell University)

  • J. Wang

    (Cornell University)

Abstract

The aim of this note is to provide an original proof and derive fine properties of the excessive function that characterizes the Laplace transform of the downward first hitting time to a fixed level of a non-degenerate continuous-time branching process. It hinges on a recent result by Choi and Patie (2016) on the potential theory of skip-free Markov chains and reveals, in particular, that the fundamental excessive function that characterizes the first hitting time is a purely excessive function.

Suggested Citation

  • F. Avram & P. Patie & J. Wang, 2019. "Purely Excessive Functions and Hitting Times of Continuous-Time Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 391-399, June.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:2:d:10.1007_s11009-018-9616-5
    DOI: 10.1007/s11009-018-9616-5
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    References listed on IDEAS

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    1. Duhalde, Xan & Foucart, Clément & Ma, Chunhua, 2014. "On the hitting times of continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4182-4201.
    2. Sagitov, Serik, 2017. "Tail generating functions for extendable branching processes," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1649-1675.
    3. Picard, Philippe & Lefevre, Claude, 1998. "The moments of ruin time in the classical risk model with discrete claim size distribution," Insurance: Mathematics and Economics, Elsevier, vol. 23(2), pages 157-172, November.
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    Cited by:

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