Weak convergence of continuous-state branching processes with large immigration

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 eith...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 179; p. 104497
Main Authors Foucart, Clément, Yuan, Linglong
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2025
Subjects
Continuous-state branching process
Extremal process
Functional limit theorem
Immigration
Regularly varying function
Shot noise process
Subordinator
secondary
Shot noise process
Immigration
Continuous-state branching process
Functional limit theorem
Subordinator
Regularly varying function
Extremal process
primary
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Summary: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.
ISSN:0304-4149
DOI:10.1016/j.spa.2024.104497