收稿日期: 2015-03-03
修回日期: 2015-05-18
网络出版日期: 2016-03-15
基金资助
Supported by National Natural Science Foundation of China(11171342)
Law of iterated logarithm of Galton-Watson processes in varying environment
Received date: 2015-03-03
Revised date: 2015-05-18
Online published: 2016-03-15
Supported by
Supported by National Natural Science Foundation of China(11171342)
南晓杰 . 变化环境中Galton-Watson过程的重对数律[J]. 中国科学院大学学报, 2016 , 33(2) : 145 -149 . DOI: 10.7523/j.issn.2095-6134.2016.02.001
By the Berry-Esseen lemma and an important extension of the conditional Borel-Cantelli lemma (Asmussen, Trans Am Math Soc,1977,231:233), we obtain the law of the iterated logarithm of the branching processes in varying environment under the condition that the second moment of the number of the offspring of each individual of each generation is uniformly upper/lower bounded. Further more, the condition is weaker than that of Gao(Gao, UCAS, Thesis 2011).
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