【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=1ⁿ X_k,M_n=maxk≤n|S_k|,n≥1.假设σ²=EX₁²+2∑_k=2^∞EX₁X_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（π²n/（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。更多还原

【Abstract】 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 σ² =EX₁² +2 sum from k=2 to ∞ EX₁X_k>0. We study theprecise 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（π²n/（8loglogn））^1/2} as ∈ ∞. The results are related to the convergence rates ofthe law of the iterated logarithm and the Chung type law of the iterated logarithm.更多还原