变化环境中Galton-Watson过程的重对数律

Law of iterated logarithm of Galton-Watson processes in varying environment

借助Berry-Esseen引理和Asmussen对条件Borel—Cantelli引理的重要推广，在变化环境中上临界分枝过程的每一代每一个个体的后代个体总数的2阶矩有一致上下界的情况下，得到变化环境中分枝过程的重对数律，从而改进了在相应的2＋6阶矩有限条件下的证明．

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）.