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arXiv · 2311.04045

Weak convergence of continuous-state branching processes with large immigration

Clément Foucart·Linglong Yuan
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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.

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Clément Foucart, Linglong Yuan. 2023-11-07. Weak convergence of continuous-state branching processes with large immigration. https://arxiv.org/abs/2311.04045

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