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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| Published in | Stochastic processes and their applications Vol. 179; p. 104497 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.01.2025
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| Subjects | |
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| ISSN | 0304-4149 |
| DOI | 10.1016/j.spa.2024.104497 |
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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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| AbstractList | 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. |
| ArticleNumber | 104497 |
| Author | Foucart, Clément Yuan, Linglong |
| Author_xml | – sequence: 1 givenname: Clément surname: Foucart fullname: Foucart, Clément email: clement.foucart@polytechnique.edu organization: CMAP, Ecole Polytechnique, IP Paris, Palaiseau, France – sequence: 2 givenname: Linglong surname: Yuan fullname: Yuan, Linglong email: linglong.yuan@liverpool.ac.uk organization: Department of Mathematical Sciences, University of Liverpool, Liverpool, UK |
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| Cites_doi | 10.1016/j.bulsci.2008.10.001 10.1016/j.spa.2014.07.019 10.1016/j.spa.2017.04.012 10.1017/apr.2021.43 10.1007/s10687-011-0131-0 10.1016/j.spa.2012.03.012 10.1016/j.spa.2013.03.010 10.1016/j.spa.2018.11.016 10.1090/S0002-9904-1972-12938-0 10.1287/moor.5.1.67 10.1214/18-AIHP909 10.2307/1426767 |
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| Keywords | secondary Shot noise process Immigration Continuous-state branching process Functional limit theorem Subordinator Regularly varying function Extremal process primary |
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| Snippet | Functional limit theorems are established for continuous-state branching processes with immigration (CBIs), where the reproduction laws have finite first... |
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| SubjectTerms | Continuous-state branching process Extremal process Functional limit theorem Immigration Regularly varying function Shot noise process Subordinator |
| Title | Weak convergence of continuous-state branching processes with large immigration |
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