Functional law of large numbers and central limit theorem for Crump-Mode-Jagers branching processes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913993792159744 |
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| author | Dramé, Ibrahima Pardoux, Etienne |
| author_facet | Dramé, Ibrahima Pardoux, Etienne |
| contents | We establish a Law of Large Numbers and a Central Limit Theorem for a class of Crump Mode Jagers continuous time branching processes, where the birth rate is age dependent, and also random (different from one individual to the next), in the limit of a large number of ancestors. The only difficulty concerns the tightness in the Skorohod space $D$ for the central limit theorem. We exploit a criterion for the CLT in $D$ due to M. Hahn \cite{MH}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12058 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional law of large numbers and central limit theorem for Crump-Mode-Jagers branching processes Dramé, Ibrahima Pardoux, Etienne Probability We establish a Law of Large Numbers and a Central Limit Theorem for a class of Crump Mode Jagers continuous time branching processes, where the birth rate is age dependent, and also random (different from one individual to the next), in the limit of a large number of ancestors. The only difficulty concerns the tightness in the Skorohod space $D$ for the central limit theorem. We exploit a criterion for the CLT in $D$ due to M. Hahn \cite{MH}. |
| title | Functional law of large numbers and central limit theorem for Crump-Mode-Jagers branching processes |
| topic | Probability |
| url | https://arxiv.org/abs/2508.12058 |