Functional law of large numbers and central limit theorem for Crump–Mode–Jagers branching processes
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}.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Statistics & Probability Letters
- Volume
- 239
- Pages
- 110916–110916
- Publication date
- 22 July 2026
- Language
- EN