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Coalescence times for critical Galton–Watson processes with immigration

Author

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  • Liu, Rong-Li
  • Ren, Yan-Xia
  • Wang, Yingrui

Abstract

Let XnI be the coalescence time of two particles picked at random from the nth generation of a critical Galton–Watson process with immigration, and let AnI be the coalescence time of the whole population in the nth generation. In this paper, we study the limiting behaviors of XnI and AnI as n→∞.

Suggested Citation

  • Liu, Rong-Li & Ren, Yan-Xia & Wang, Yingrui, 2024. "Coalescence times for critical Galton–Watson processes with immigration," Statistics & Probability Letters, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:stapro:v:210:y:2024:i:c:s0167715224000907
    DOI: 10.1016/j.spl.2024.110121
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    References listed on IDEAS

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    1. Athreya, K.B., 2012. "Coalescence in the recent past in rapidly growing populations," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3757-3766.
    2. Durrett, R., 1978. "The genealogy of critical branching processes," Stochastic Processes and their Applications, Elsevier, vol. 8(1), pages 101-116, November.
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