| NA序列重对数律的几个极限定理 |
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| 引用本文： | 张立新.NA序列重对数律的几个极限定理[J].数学学报,2004,47(3):541-552. |
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| 作者姓名： | 张立新 |
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| 作者单位： | 浙江大学,西溪校区,数学系,杭州,310028 |
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| 基金项目： | 国家自然科学基金(10071072) |
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| 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。
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| 关 键 词： | 重对数律 Chung重对数律 负相伴 |
| 文章编号： | 0583-1431(2004)03-0541-12 |
Some Limit Results on the Law of the Iterated Logarithm of NA Sequences |
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| Li Xin ZHANG.Some Limit Results on the Law of the Iterated Logarithm of NA Sequences[J].Acta Mathematica Sinica,2004,47(3):541-552. |
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| Authors: | Li Xin ZHANG |
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| Institution: | Li Xin ZHANG Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China |
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| 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 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. |
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| Keywords: | The law of the iterated logarithm Chung's law of the iterated logarithm Negative association |
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