两两NQD列的极限定理∗

摘要

In this paper, we study the complete convergence properties and strong laws of large numbers for pairwise NQD random sequences. We present the definition of pairwise NQD random sequences and the Kolmogorov inequality to the case of pairwise NQD random sequences. Based on the Kolmogorov inequality, we obtain complete convergence properties of pairwise NQD random sequences. We construct two non-increasing functions based on the properties of non-increasing function, and obtain some strong laws of large number for pairwise NQD random sequences, which is similar to independent random variable sequences. The theorem obtained in this paper thus inclines to extend the related results presented in previous literatures.%本文主要研究了两两NQD列的完全收敛性和强大数定律。文中给出了两两NQD列的定义和推广的Kolmogorov型不等式，并利用推广的Kolmogorov型不等式，得到了两两NQD列的完全收敛性定理。本文构造了两个不增函数，利用不增函数的性质，得到了两两NQD列的强大数定律。本文得到的强大数定律与独立随机变量情况下的强大数定律相类似，进而推广了前人的研究成果。