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Tail generating functions for extendable branching processes

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  • Sagitov, Serik

Abstract

We study branching processes of independently splitting particles in the continuous time setting. If time is calibrated such that particles live on average one unit of time, the corresponding transition rates are fully determined by the generating function f for the offspring number of a single particle. We are interested in the defective case f(1)=1−ϵ, where each splitting particle with probability ϵ is able to terminate the whole branching process. A branching process {Zt}t≥0 will be called extendable if f(q)=q and f(r)=r for some 0≤q

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  • Sagitov, Serik, 2017. "Tail generating functions for extendable branching processes," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1649-1675.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:5:p:1649-1675
    DOI: 10.1016/j.spa.2016.09.004
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    References listed on IDEAS

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    1. Cohn, H. & Hering, H., 1983. "Inhomogeneous Markov branching processes: Supercritical case," Stochastic Processes and their Applications, Elsevier, vol. 14(1), pages 79-91, January.
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    Cited by:

    1. 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.
    2. J. Hüsler & M. G. Temido & A. Valente-Freitas, 2022. "On the Maximum of a Bivariate INMA Model with Integer Innovations," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2373-2402, December.

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