ON THE ASYMPTOTIC PATTERNS OF SUPERCRITICAL BRANCHING PROCESSES IN VARYING ENVIRONMENTS
成果类型：
Article
署名作者：
Cohn, Harry
署名单位：
University of Melbourne
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
896-902
关键词：
摘要：
Let {Zn} be a branching process whose offspring distributions vary with n. It is shown that the sequence {max(i > 0) P(Z(n) = i)} has a limit. Denote this limit by M. It turns out that M is positive only if the offspring variables rapidly approach constants. Let {c(n)} be a sequence of constants and Wn sZnrcn. It will be proven that M = 0 is necessary and sufficient for the limit distribution functions of all convergent {W-n} to be continuous on (0,infinity). If M > 0 there is, up to an equivalence, only one sequence {c(n)} such that {W-n} has a limit distribution with jump points in (0,infinity) Necessary and sufficient conditions for continuity of limit distributions are derived in terms of the offspring distributions of {Zn}.