B-统计-α-可积与大数定律

B-statistical α-integrability and laws of large numbers

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).