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Linear-fractional branching processes with countably many types

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  • Sagitov, Serik

Abstract

We study multi-type Bienaymé–Galton–Watson processes with linear-fractional reproduction laws using various analytical tools like the contour process, spinal representation, Perron–Frobenius theorem for countable matrices, and renewal theory. For this special class of branching processes with countably many types we present a transparent criterion for R-positive recurrence with respect to the type space. This criterion appeals to the Malthusian parameter and the mean age at childbearing of the associated linear-fractional Crump-Mode-Jagers process.

Suggested Citation

  • Sagitov, Serik, 2013. "Linear-fractional branching processes with countably many types," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2940-2956.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:8:p:2940-2956
    DOI: 10.1016/j.spa.2013.03.008
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    References listed on IDEAS

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    1. Sagitov, Serik, 1995. "A key limit theorem for critical branching processes," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 87-100, March.
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    Cited by:

    1. Tan, Jiangrui & Li, Junping, 2023. "Recurrence property for Galton–Watson processes in which individuals have variable lifetimes," Statistics & Probability Letters, Elsevier, vol. 199(C).
    2. Popovic, Lea & Rivas, Mariolys, 2014. "The coalescent point process of multi-type branching trees," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4120-4148.
    3. Braunsteins, Peter & Decrouez, Geoffrey & Hautphenne, Sophie, 2019. "A pathwise approach to the extinction of branching processes with countably many types," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 713-739.

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