NA序列重对数律的几个极限定理  

Some Limit Results on the Law of the Iterated Logarithm of NA Sequences

作　　者：张立新[1] 

机构地区：[1]浙江大学(西溪校区)数学系,杭州310028

出　　处：《数学学报（中文版）》2004年第3期541-552,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(10071072)

摘　　要：设{X_n;n≥1}均值为零、方差有限的NA平稳序列。记S_n=∑_(k=1)~n X_k,M_n=maxk≤n|S_k|,n≥1.假设σ~2=EX_1~2+2∑_(k=2)~∞EX_1X_k>0。本文讨论了:当ε 0时,P{M_n≥εσ(2nloglogn)^(1/2)的一类加权级数的精确渐近性质,以及当ε∞时,P{M_n≤εσ(π~2n/(8loglogn))^(1/2)}的一类加权级数的精确渐近性质。这些性质与重对数律和Chung重对数律的速度有关。Let {X_n;n≥ 1} be a strictly stationary sequence of negatively associ- ated random variables with mean zeros and finite variances. Set S_n=sum from k=1 to n X_k, M_n =max_k≤n |S_k|, n≥1. Suppose σ~2 =EX_1~2 +2 sum from k=2 to ∞ EX_1X_k>0. We study the precise asymptotics of a kind of weighted infinite series of P{M_n≥∈σ(2n loglogn)^(1/2)} as ∈ 0, and the precise asymptotics of a kind of weighted infinite series of P{M_n≤ ∈σ(π~2n/(8loglogn))^(1/2)} as ∈ ∞. The results are related to the convergence rates of the law of the iterated logarithm and the Chung type law of the iterated logarithm.

关 键 词：重对数律 CHUNG重对数律 负相伴 

分 类 号：O211.4[理学—概率论与数理统计]