B值m相依随机变量序列完全收敛性的精确渐进性  

Precise Asymptotics of the Complete Convergence for m-Dependent Banach Space Valued Random Variables

作　　者：张勇[1] 杨晓云[1] 

机构地区：[1]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2006年第1期1-8,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10271049)

摘　　要：设{Xn;n≥1}为均值为零、方差有限的B值m相依随机变量列.利用B值m相依随机变量列弱收敛定理讨论了{Xn;n≥1}的完全收敛性及重对数律的精确渐进性.若记Sn=∑nj=1Xj,1≤p<2,得到了P{‖Sn‖≥εn1/p}的一类加权级数在→0时的极限以及P{‖Sn‖≥εnlogn}的一类加权级数在→0时的极限.所得结果是实值i.i.d.随机变量序列完全收敛性及重对数律的精确渐进性质的进一步推广.Let {Xn;n≥1} zeros and finite variances, random variables, we studi a sequence of m-dependent Banach space valued random variables with mean y using the weak convergence theorem of m-dependent Banach space valued the precise asymptotics of the complete convergence and the law of the iterated logarithm for the sequence {Xn;n≥1}.Set Sn=n∑（j=1）Xj,1≤P〈2,we have the limits of a weighed infinite series of P{｜｜Sn｜｜≥εn^1/p} as ε→0 and the limits of a kind of weighed infinite series of P{｜｜Sn｜｜≥ε√nlog n} as ε→0 We extended the results of the precise asymptotics of the complete convergence and the law of the iterated logarithm for real valued i. i. d. random variables.

关 键 词：m相依随机元 完全收敛性 精确渐进性 

分 类 号：O211.4[理学—概率论与数理统计]