Convergence Rates of Tail Probabilities for Sums under Dependence Assumptions  

作　　者：Xiao Rong YANG Wei Dong LIU Ke Ang FU Lin Xin ZHANG 

机构地区：[1]School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, P. R. China [2]Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China [3]School of Statistics and Mathematics, Zhejiang Gongshang University, Han qzhou 310018, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第8期1591-1600,共10页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant Nos. 10771192 and 10671176) 1)

摘　　要：Let {X,X1,X2,……}be a zero mean strictly stationary Ф-mixing sequence. Set Sn=∑n k=1 and f（x^p）=∑∞n=1 n^r-2P（｜Sn｜≥x^p√ES2nlog n）,When ε〉（√2）1/p,for p〉1/2 and r〉1,the conditions for ∫∞ε f（x^p）dx 〈∞ to hold is established, by using coupled methods together withstrong approximation, which are different from the traditional symmetrization and Hoffman-JФrgensen inequality.Let {X,X1,X2,……}be a zero mean strictly stationary Ф-mixing sequence. Set Sn=∑n k=1 and f（x^p）=∑∞n=1 n^r-2P（｜Sn｜≥x^p√ES2nlog n）,When ε〉（√2）1/p,for p〉1/2 and r〉1,the conditions for ∫∞ε f（x^p）dx 〈∞ to hold is established, by using coupled methods together withstrong approximation, which are different from the traditional symmetrization and Hoffman-JФrgensen inequality.

关 键 词：Complete convergence mixing sequences strong approximation 

分 类 号：O212.1[理学—概率论与数理统计] O211.5[理学—数学]