摘要
本文探讨了随机变量序列依概率收敛与依分布收敛的关系 ,并给出了一个依分布收敛能保证依概率收敛的最弱的条件 ,即 :设分布函数列 { Fn(x) }弱收敛于连续的分布函数 F(x) ,则存在随机变量序列{ξn}和随机变量ξ,它们分别以 { Fn(x) }和 F(x)为其对应的分布函数列和分布函数 ,且 {ξn}依概率收敛于ξ.
In this paper, the relation between the convergence in probability of a sequences of random variables and its convergence in distribution is discussed. A most weak condition is given under which the convegence in distribution of a sequences of random variables can garrentee its convergence in probability. i.e, let a sequences of distribution functions {F n(x)} converge weakly to a continuous distribution function F(x), then there exit a sequences of random veriables {ξ n} and a random variable ξ corresponding to {F n(x)} and F(x), respectively, and {ξ n} converges in probabily to ξ.
出处
《工科数学》
2001年第5期41-44,共4页
Journal of Mathematics For Technology
关键词
随机变量
分布函数
弱收敛
依概率收敛
依分布收敛
random variable
distribution function
weak convergence
convergence in probability
convergence in distribution
