Asymptotic normality in Crump-Mode-Jagers processes: the lattice case

TL;DR

This paper proves that in a supercritical lattice Crump-Mode-Jagers process, the fluctuations of the age distribution are asymptotically normal under a specific offspring intensity condition, extending results to populations with random characteristics.

Contribution

It establishes the asymptotic normality of second-order fluctuations in lattice Crump-Mode-Jagers processes under a key offspring intensity condition, including populations with random characteristics.

Findings

Fluctuations are asymptotically normal under the specified condition.

The condition on offspring intensity is essential for normality.

Results extend to populations with random characteristics.

Abstract

Consider a supercritical Crump--Mode--Jagers process such that all births are at integer times (the lattice case). We show that under a certain condition on the intensity of the offspring process, the second-order fluctuations of the age distribution are asymptotically normal; the condition is essential and not just a technicality. This extends to populations counted by a random characteristic.