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

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

doi:10.1017/apr.2020.35

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

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

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

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 language	English
Pages (from-to)	1127-1163
Number of pages	37
Journal	Advances in Applied Probability
Volume	52
Issue number	4
DOIs	https://doi.org/10.1017/apr.2020.35
Publication status	Published - 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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10.1017/apr.2020.35Licence: Unspecified

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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. ",

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N2 - 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.

AB - 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.

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

Abstract

Keywords

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Other files and links

Measure-valued analysis of stochastic populations

Stochastic Populations: Theory and Applications

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

Abstract

Keywords

Access to Document

Other files and links

Projects

Measure-valued analysis of stochastic populations

Stochastic Populations: Theory and Applications

Cite this