B-统计-α-可积与大数定律  

B-statistical α-integrability and laws of large numbers

作　　者：陈梦如 汪忠志[2] 彭维才[3] CHEN Meng-ru;WANG Zhong-zhi;PENG Wei-cai(Dept.of Basic,Wanjiang Univ.of Tech.,Ma’anshan 243000,China;Sch.of ME.and Data Sci.,AnHui Univ.of Tech.,Ma’anshan,243000,China;Sch.of Math.and Big Data,Chaohu Univ.,Hefei 238000,China)

机构地区：[1]皖江工学院基础部,安徽马鞍山243000 [2]安徽工业大学微电子与数据科学学院,安徽马鞍山243000 [3]巢湖学院数学与大数据学院,安徽合肥238000

出　　处：《高校应用数学学报（A辑）》2023年第4期398-406,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家社会科学基金(21BJY213);安徽省社会科学创新发展研究项目(2021CX077);安徽省自然科学基金高校重点项目(KJ2021A0386,KJ2021A1031,KJ2021A1032);安徽省研究生学术创新项目(2022xscx071)。

摘　　要：提出了若干关于{a_(ni)}的B-统计可积性的新概念,即B-统计-α-可积(BI(α)),残差B-统计-α-可积(RBI(α))和残差B-统计-(α,p)-可积(RBI(α,p)),推广了Cabrera等建立的关于{a_(nk)}的B-统计一致可积性,并且此三种可积的条件依次减弱.对于两两独立的随机变量序列,在新的B-统计可积条件下,得到了关于∑_(i=1)^(∞)a_(ni)(X_(i)-EX_(i))的统计意义上的p阶平均收敛定理.最后,对一类特殊的相依随机变量序列,获得了关于∑_(i=1)^(∞)a_(ni)X_(i)的统计收敛定理.In this study,some new concepts of B-statistical integrability with respect to{a_(ni)}were given,namely B-statistical α-Integrability(BI(α)),Residual B-statistical α-Integrability(RBI(α))and the Residual B-statistical(α,p)-Integrability(RBI(α,p)).And their conditions become weaker one by one,and all of them are strictly weaker than B-statistical uniform integrability with respect to{a_(nk)},which is investigated by Cabrera et al.(2020).For a sequence of pairwise independent random variables,these weaker conditions of B-statistical integrability,are sufficient for the law of large numbers with mean convergence in the statistical sense to hold for ∑_(i=1)^(∞)a_(ni)(X_(i)-EX_(i)).For some special kinds of dependent sequences of random variables,similar convergence in the statistical sense are obtained for Emiani ∑_(i=1)^(∞)a_(ni)X_(i).

关 键 词：随机变量序列 B-统计可积 统计收敛 

分 类 号：O211.4[理学—概率论与数理统计]