Convergence of the age structure of general schemes of population processes

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Abstract

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→∞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.

Original languageEnglish
Pages (from-to)893-926
Number of pages34
JournalBernoulli
Volume26
Issue number2
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • Age-structure dependent population processes
  • Carrying capacity
  • Central limit theorem

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