Remaining-lifetime age-structured branching processes
Probability
2024-01-08 v1
Abstract
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models without or with immigration are constructed as measure-valued processes by pathwise unique solutions of stochastic equations driven by time-space Poisson random measures. In the subcritical branching case, we give a sufficient condition for the ergodicity of the process with immigration. Two large number laws and a central limit theorem of the occupation times are proved.
Cite
@article{arxiv.2401.02462,
title = {Remaining-lifetime age-structured branching processes},
author = {Ziling Cheng and Zenghu Li},
journal= {arXiv preprint arXiv:2401.02462},
year = {2024}
}