Limit theorems for multi-type general branching processes with population dependence

Jie Yen Fan, Kais Hamza, Peter Jagers, Fima C. Klebaner

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Abstract

A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population as a measure-valued process and obtain its asymptotics as the population grows with the environmental carrying capacity. Thus, a deterministic approximation is given, in the form of a law of large numbers, as well as a central limit theorem. This general framework is then adapted to model sexual reproduction, with a special section on serial monogamic mating systems.

Original languageEnglish
Pages (from-to)1127-1163
Number of pages37
JournalAdvances in Applied Probability
Volume52
Issue number4
DOIs
Publication statusPublished - Dec 2020

Keywords

  • Age and type structure dependent population processes
  • carrying capacity
  • central limit theorem
  • diffusion approximation
  • law of large numbers
  • size dependent reproduction

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