随机变量序列几乎处处收敛的几个等价命题  

Several Equivalent Propositions on Almost Sure Convergence of Random Variables

作　　者：钟镇权[1] 

机构地区：[1]玉林师范学院数学与计算机科学系,广西玉林537000

出　　处：《三峡大学学报（自然科学版）》2005年第2期183-185,共3页Journal of China Three Gorges University：Natural Sciences

摘　　要：由随机变量序列几乎处处收敛可推出其依概率收敛,进而可推出其依分布收敛,可见判别几乎处处收敛的重要性.给出了它的几个等价命题,同时还证明了独立随机变量和序列几乎处处收敛等价于依概率收敛,亦等价于依分布收敛.Through almost sure convergence of random variables, the probability convergence can be derived; and further the weak convergence can be derived.This paper gaves its equivalent propositions and proves that a.s. convergence of independent random variables’s sum variables is equivalent to its probability convergence, and equivalent to its weak convergence.

关 键 词：几乎处处收敛 随机变量序列 等价命题 独立随机变量和 依概率收敛 依分布收敛 推出 可见 

分 类 号：O211.4[理学—概率论与数理统计] O211.5[理学—数学]