随机变量阵列的一个强大数律  

A Strong Logarithmic Law for Arrays of Random Variables

作　　者：邵杰[1] 

机构地区：[1]辽东学院经济学院,辽宁丹东118001

出　　处：《辽东学院学报（自然科学版）》2014年第1期53-56,共4页Journal of Eastern Liaoning University:Natural Science Edition

摘　　要：随机变量序列的大数定律在概率极限理论和数理统计中扮演着重要的角色,经典的大数律主要是研究独立同分布的随机变量序列,后来许多学者致力于减弱独立同分布这一条件,或将随机变量序列推广到随机变量阵列.文章主要研究任意随机变量阵列的强大数律,利用Borel-Cantelli引理和鞅差序列的结论,通过推理论证,得到了任意随机变量阵列的一个强大数律,并且作为特例,得到了随机变量序列加权和的强大数律.Law of large numbers for sequences of random variables plays an important role in the limit proba -bility theory and mathematical statistics .Classic law of large numbers was mainly about independent and identically distributed random variable sequences .Many scholars are devoted to weaken the condition of independence and i-dentical distribution and extend the sequence of random variables to array of random variables .In this study , the author obtains a strong law for arrays of random variables by using the conclusion of Borel -Cantelli lemma and martingale difference sequence .Furthermore, as a special case , a strong law for the sequence of weighted sums is accordingly gotten .

关 键 词：随机变量阵列 强大数律 鞅差 

分 类 号：O211.6[理学—概率论与数理统计]