两两NQD序列的对数平均大数定律

Law of Large Numbers of Logarithmic Average for Pairwise NQD Sequences

在一定条件下,证明了两两NQD序列的对数平均弱大数定律,所得结果推广了已有文献中关于NA序列的相关结论.经典的大数定律主要研究随机变量序列的算数平均值的收敛性,而对数平均收敛弱于算数平均收敛,因此,对数平均大数定律的研究拓展了概率极限理论研究的范围.

Under certain conditions, a weak law of large numbers of logarithmic average for pairwise NQD sequences is proven and the results obtained here extends the corresponding results in previous literature. The classical law of large numbers is chiefly focused on the convergence of arithmetical mean of random variable sequences. Since the convergence of logarithmic average is weaker than the convergence of arithmetical average, the study of logarithmic average law of large numbers expands the scope of probability limit theory study.