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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
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)
关键词
重对数律
CHUNG重对数律
负相伴
The law of the iterated logarithm
Chung's law of the iterated logarithm
Negative association
