Functional law of large numbers and central limit theorem for Crump-Mode-Jagers branching processes

Ibrahima Dramé; Etienne Pardoux

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arXiv · 2508.12058

Functional law of large numbers and central limit theorem for Crump-Mode-Jagers branching processes

Ibrahima Dramé·Etienne Pardoux

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Abstract

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}.

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Ibrahima Dramé, Etienne Pardoux. 2025-08-16. Functional law of large numbers and central limit theorem for Crump-Mode-Jagers branching processes. https://arxiv.org/abs/2508.12058

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