Harmonic moments and large deviation rates for supercritical branching processes

• 成果类型: Article
• 署名作者: Ney, PE; Vidyashankar, AN
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University System of Georgia; University of Georgia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2003
• 页码: 475-489
• 关键词: migrating binomial observations

摘要

Let {Z(n), n greater than or equal to 1) be a single type supercritical Galton-Watson process with mean EZ(1) equivalent to m initiated by a single ancestor. This paper studies the large deviation behavior of the sequence {R-n equivalent to (Zn)-(Zn+1) : n greater than or equal to 1} and establishes a phase transition in rates depending on whether r, the maximal number of moments possessed by the offspring distribution, is less than, equal to or greater than the Schroder constant alpha. This is done via a careful analysis of the harmonic moments of Z(n)