Branching processes with dependence but homogeneous growth

• 成果类型: Article
• 署名作者: Jagers, P
• 署名单位: Chalmers University of Technology; University of Gothenburg
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1999
• 页码: 1160-1174
• 关键词: galton-watson processes; asymptotic-behavior; population

摘要

A (general) branching process, where individuals need not reproduce independently, satisfies a homogeneous growth condition if, vaguely, one would not expect the progeny from any one individual to make out more than its proper fraction of the whole population at any time in the future. This notion is made precise, and it is shown how it entails classical Malthusian growth in supercritical cases, in particular for population size-dependent Bienayme-Galton-Watson and Markov branching processes, and for nondecreasing age-dependent processes with continuous life span distributions.