Limit theorems for multi-type general branching processes with population dependence. (December 2020)

• Record Type: Journal Article
• Authors: Fan, Jie Yen; Hamza, Kais; Jagers, Peter; Klebaner, Fima C.
• Is Part Of: Advances in applied probability. Volume 52:Number 4(2020)
• Page Start: 1127
• Page End: 1163
• Publication Date: 2020-12
• Subjects: Age and type structure dependent population processes, -- size dependent reproduction, -- carrying capacity, -- law of large numbers, -- central limit theorem, -- diffusion approximation; 60J80, -- 60F05, -- 92D25; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2020.35
• Languages: English
• ISSNs: 0001-8678

Abstract

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.