CONCEPTUAL PROOFS OF L-LOG-L CRITERIA FOR MEAN-BEHAVIOR OF BRANCHING-PROCESSES

• 成果类型: Article
• 署名作者: LYONS, R; PEMANTLE, R; PERES, Y
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988176
• 发表日期: 1995
• 页码: 1125-1138
• 关键词: trees; cluster

摘要

The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, shelving that an L log L condition is decisive. In critical and subcritical cases, results of Kolmogorov and later authors give the rate of decay of the probability that the process survives at least n generations. We give conceptual proofs of these theorems based on comparisons of Galton-Watson measure to another measure on the space of trees. This approach also explains Yaglom's exponential limit law for conditioned critical branching processes via a simple characterization of the exponential distribution.