Asymptotic fluctuations in supercritical multi-type Crump-Mode-Jagers processes

Konrad Kolesko; Alicja Kołodziejska; Matthias Meiners

Asymptotic fluctuations in supercritical multi-type Crump-Mode-Jagers processes

Probability 2026-07-24 v1

Authors: Konrad Kolesko , Alicja Kołodziejska , Matthias Meiners

Abstract

We consider an irreducible, supercritical multi-type general branching process (Crump-Mode-Jagers process) with finite type space, counted with random characteristic. We prove that, under certain second moment assumptions, a central limit theorem holds for the process. Our result extends the single-type central limit theorem obtained recently in [Ann. Probab. 52 (2024), no. 4, 1538-1606] and unifies various limiting results for specific branching processes.

Keywords

Crump-Mode-Jagers processes central limit theorem multi-type branching processes supercritical random characteristic asymptotic fluctuations

Cite

@article{arxiv.2607.22414,
  title  = {Asymptotic fluctuations in supercritical multi-type Crump-Mode-Jagers processes},
  author = {Konrad Kolesko and Alicja Kołodziejska and Matthias Meiners},
  journal= {arXiv preprint arXiv:2607.22414},
  year   = {2026}
}