随机变量序列部分和的几乎必然收敛性

Almost Sure Convergence for the Partial Sums of Random Variable Sequence

设{Xn,n>1}是任意的随机变量序列.胡舒合等在二阶矩限制下,获得了任意随机变量序列的Hajek-Renyi型不等式,并给出了随机变量序列部分和收敛的强大数定律.本文利用胡舒合等获得的强大数定律,给出了随机变量序列部分和的一些几乎必然收敛性,并给出了结果在PA、NA和两两NQD序列场合下的应用.

Let ｜Xn, n≥1｜ be a random variable sequence. Hu Shu-he et al. obtained the Hajek-Renyi-Type inequality and strong law of large numbers for the partial sums of random variable sequences under second moment conditions. This article gives some almost sure convergence properties for the partial sums of random variable sequence by using the strong law of large numbers, which were obtained by Hu. Some applications for the PA, NA sequences and pairwise negatively quadrant dependent sequences are given.