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| R/S统计量重对数律的精确收敛速度 | |
| 引用本文： | 吴红梅,闻继威. R/S统计量重对数律的精确收敛速度[J]. 高校应用数学学报(英文版), 2006, 21(4): 461-466. DOI: 10.1007/s11766-006-0010-7 |
| 作者姓名： | 吴红梅 闻继威 |
| 作者单位： | 浙江大学城市学院 |
| 摘 要： | Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge. |
| 关 键 词： | R/S 统计学 尾概率 序列 任意变量 |
| 收稿时间： | 2006-03-28 |
Precise rates in the law of the iterated logarithm for R/S statistics |
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| Hongmei Wu,Jiwei Wen. Precise rates in the law of the iterated logarithm for R/S statistics[J]. Applied Mathematics A Journal of Chinese Universities, 2006, 21(4): 461-466. DOI: 10.1007/s11766-006-0010-7 | |
| Authors: | Hongmei Wu Jiwei Wen |
| Affiliation: | 1. City College of Zhejiang University, Hangzhou, 310015, China 2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China |
| Abstract: | Let {X n; n ≥ 1} be a sequence of i.i.d. random variables with finite variance, Q(n) be the related R/S statistics. It is proved that $$mathop {lim }limits_{varepsilon searrow 0} varepsilon ^2 sumlimits_{n = 1}^infty {frac{1}{{n log n}}Pleft{ {Q(n) geqslant varepsilon sqrt {2n log log n} } right} = frac{1}{2}EY^2 } $$ , where Y = sup0<t≤1 B(t) ? inf0≤t≤s B(t), and B(t) is a Brownian bridge. |
| Keywords: | law of the iterated logarithm R/S statistics tail probability |
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