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

2025/08/16 by Ibrahima Dramé, Dramé, Ibrahima, Etienne Pardoux +1
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.12058

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 \citeMH.

Citations

• A Crump-Mode-Jagers Branching Process Model of Prion Loss in Yeast
• Embedding of Urn Schemes into Continuous Time Markov Branching Processes and Related Limit Theorems

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