Local limit theory and large deviations 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
• DOI: 10.1214/105051604000000242
• 发表日期: 2004
• 页码: 1135-1166
• 关键词: galton-watson process; EVOLUTION; tests

摘要

In this paper we study several aspects of the growth of a supercritical Galton-Watson process {Z(n) : n greater than or equal to 1}, and bring out some criticality phenomena determined by the Schroder constant. We develop the local limit theory of Z(n), that is, the behavior of P(Z(n) = v(n)) as v(n) NE arrow infinity, and use this to study conditional large deviations of {Y-Zn : n greater than or equal to 1}, where Y-n satisfies an LDP, particularly of {Z(n)(-1) Z(n+1) : n greater than or equal to 1} conditioned on Z(n) greater than or equal to v(n).