Convergence of the age structure of general schemes of population processes
Journal article, 2020

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 [8] the Law of Large Numbers as K Ñ 8 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.

carrying capacity

central limit theo- rem.

Age-structure dependent population processes

Author

Peter Jagers

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Jie Yen Fan

Monash University

K. Hamza

Monash University

Fima C. Klebaner

Monash University

Bernoulli

1350-7265 (ISSN)

Vol. 26 2 893-926

Subject Categories

Evolutionary Biology

Probability Theory and Statistics

Roots

Basic sciences

DOI

10.3150/18-BEJ1100

More information

Latest update

3/2/2020 9