随机变量序列的各种收敛性的关系

Relation among Some Convergence of a Sequences of Random Variables

主要讨论了几乎处处收敛与依概率收敛,完全收敛与几乎处处收敛的关系.给出了由依概率收敛推出几乎处处收敛的条件和由几乎处处收敛推出完全收敛的条件,从而比较完全地说明了随机变量序列的各种收敛性之间的关系.

In this paper we discuss the relation between almost sure convergence and convergence in probability,and the relation between complete convergence and almost sure convergence.A condition is given under which the convergence in probability of a consequence of random variables can grantee almost sure convergence, and another condition is given under which the almost sure convergence can grantee complete convergence.Hence we obtain completely the relation among some convergence of a sequences of random variables.