Open Access
May 2020 Convergence of the age structure of general schemes of population processes
Jie Yen Fan, Kais Hamza, Peter Jagers, Fima Klebaner
Bernoulli 26(2): 893-926 (May 2020). DOI: 10.3150/18-BEJ1100


We consider a family of general branching processes with reproduction parameters depending on the age of the individual as well as the population age structure and a parameter $K$, which may represent the carrying capacity. These processes are Markovian in the age structure. In a previous paper (Proc. Steklov Inst. Math. 282 (2013) 90–105), the Law of Large Numbers as $K\to \infty $ was derived. Here we prove the central limit theorem, namely the weak convergence of the fluctuation processes in an appropriate Skorokhod space. We also show that the limit is driven by a stochastic partial differential equation.


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Jie Yen Fan. Kais Hamza. Peter Jagers. Fima Klebaner. "Convergence of the age structure of general schemes of population processes." Bernoulli 26 (2) 893 - 926, May 2020.


Received: 1 September 2017; Revised: 1 November 2018; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166551
MathSciNet: MR4058355
Digital Object Identifier: 10.3150/18-BEJ1100

Keywords: age-structure dependent population processes , carrying capacity , central limit theorem

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 2 • May 2020
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