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Weak convergence of continuous-state branching processes with large immigration

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  • Foucart, Clément
  • Yuan, Linglong

Abstract

Functional limit theorems are established for continuous-state branching processes with immigration (CBIs), where the reproduction laws have finite first moments and the immigration laws exhibit large tails. Different regimes of immigration are identified, leading to limiting processes that are either subordinators, CBIs, extremal processes, or extremal shot noise processes.

Suggested Citation

  • Foucart, Clément & Yuan, Linglong, 2025. "Weak convergence of continuous-state branching processes with large immigration," Stochastic Processes and their Applications, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:spapps:v:179:y:2025:i:c:s0304414924002059
    DOI: 10.1016/j.spa.2024.104497
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    References listed on IDEAS

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    1. Kella, Offer & Löpker, Andreas, 2013. "Weak convergence of subordinators to extremal processes," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3122-3131.
    2. 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.
    3. Maller, Ross & Schindler, Tanja, 2019. "Small time convergence of subordinators with regularly or slowly varying canonical measure," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4144-4162.
    4. Keller-Ressel, Martin & Mijatović, Aleksandar, 2012. "On the limit distributions of continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2329-2345.
    5. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
    6. Iksanov, Alexander & Kabluchko, Zakhar, 2018. "Functional limit theorems for Galton–Watson processes with very active immigration," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 291-305.
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