Weak convergence of continuous-state branching processes with large immigration

Clément Foucart and Linglong Yuan

Stochastic Processes and their Applications, 2025, vol. 179, issue C

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.

Keywords: Continuous-state branching process; Immigration; Functional limit theorem; Subordinator; Extremal process; Shot noise process; Regularly varying function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2024.104497

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