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

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  03 December 2020

Jie Yen Fan ,
Kais Hamza Open the ORCID record for Kais Hamza [Opens in a new window] ,
Peter Jagers  and
Fima C. Klebaner
Jie Yen Fan*
Affiliation:
Monash University
Kais Hamza*
Affiliation:
Monash University
Peter Jagers*
Affiliation:
Chalmers University of Technology and University of Gothenburg
Fima C. Klebaner*
Affiliation:
Monash University
*
*Postal address: School of Mathematics, Monash University, Clayton, VIC 3800, Australia.
*Postal address: School of Mathematics, Monash University, Clayton, VIC 3800, Australia.
***Postal address: Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Gothenburg, Sweden.
*Postal address: School of Mathematics, Monash University, Clayton, VIC 3800, Australia.
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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.

Keywords

Age and type structure dependent population processessize dependent reproductioncarrying capacitylaw of large numberscentral limit theoremdiffusion approximation

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F05: Central limit and other weak theorems 92D25: Population dynamics (general)
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 4 , December 2020 , pp. 1127 - 1163
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Copyright
© Applied Probability Trust 2020

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