ρ-混合序列的重对数律

Law of the Iterated Logarithm for ρ-Mixing Sequences

设{Xn,n≥1}是同分布ρ-混合序列,其分布属于特征指数为α(0<α<2) 的非退化稳定分布的正则吸引场,证明了依概率1有lira supn→∞ = e1/α,并获得了一系列等价条件．此结果的获得不仅将已有的一些结果推广至ρ-混合序列的情形,并且将其结果作了一定的改进．

Let {Xi,i ≥1} be p-mixing sequences with identical distributions, and these distributions belong to domain of normal attraction with non-degeneratc stable n X 1 distribution. With probability one, we have lim supn→∞（｜∑i^n=1Xi｜/n1/α）1/loglogn=e^1/α And we get several equivaent conditions, which not only generalize the obtained results equivalent to ρ- mixing sequences, but also improve them.