PRECISE RATES IN THE LAW OF THE ITERATED LOGARITHM FOR R/S STATISTICS  

作　　者：Wu Hongmei Wen Jiwei 

机构地区：[1]City College of Zhejiang University, Hangzhou 310015, China. [2]Department of Mathematics, Zhejiang University, Hangzhou, 310027, China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2006年第4期461-466,共6页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the NNSF of China(10071072).

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.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：law of the iterated logarithm R/S statistics tail probability. 

分 类 号：O21[理学—概率论与数理统计]