Harmonic continuous-time branching moments
成果类型：
Article
署名作者：
Piau, Didier
署名单位：
Universite Claude Bernard Lyon 1; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051606000000493
发表日期：
2006
页码：
2078-2097
关键词：
摘要：
We show that the mean inverse populations of nondecreasing, square integrable, continuous-time branching processes decrease to zero like the inverse of their mean population if and only if the initial population k is greater than a first threshold m(1) >= 1. If, furthermore, k is greater than a second threshold m(2) >= m(1), the normalized mean inverse population is at most 1/(k - m(2)). We express m(1) and m(2) as explicit functionals of the reproducing distribution, we discuss some analogues for discrete time branching processes and link these results to the behavior of random products involving i.i.d. nonnegative sums.