多维欧氏空间中的一般重对数律的精确速率  

Precise Rates in the Generalized Law of the Iterated Logarithm in Multidimensional Euclidean Space

作　　者：徐明周 程琨 XU Mingzhou;CHENG Kun(School of Information and Engineering,Jingdezhen Ceramic University,Jingdezhen,333403,China)

机构地区：[1]景德镇陶瓷大学信息工程学院,景德镇333403

出　　处：《应用概率统计》2021年第5期507-514,共8页Chinese Journal of Applied Probability and Statistics

基　　金：The project was supported by the Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic Institute(Grant No.102/01003002031);the Scientific Program of Department of Education of Jiangxi Province of China(Grant Nos.GJJ190732,GJJ180737);the Natural Science Foundation Program of Jiangxi Province(Grant No.20202BABL211005).

摘　　要：设{X,X_(n),n≥1}是一列满足EX=(0,0,...,0)_(m×1)和Cov(X,X)=∑独立同分布的随机向量.对任意d>0和a_(n)=o(ln ln n)^(-d)),我们得到P(|S_(n)|≥(εa_(n))σ√n(ln ln n)^(d))的一类加权无穷级数的一般重对数律的精确速率.Let {X,X_(n),n≥1} be a sequence of i.i.d.random vectors withEX=(0,0,...,0)_(m×1)和Cov(X,X)=∑,and set S_(n)=\tsm_{i=1}∑nX_(i),n≥1.For every d>0 and a_(n)=o(ln ln n)^(-d)),we obtain the precise rates in the generalized law of the iterated logarithm for a kind of weighted infiniteseries of P(|S_(n)|≥(εa_(n))σ√n(\ln ln n)^(d)).

关 键 词：精确速率 重对数律 完全收敛 独立同分布随机向量 

分 类 号：O211.4[理学—概率论与数理统计]