摘要
In discussing the convergence in probability (in distribution) of a sequence of random variables, it is often used that if for any n,P{Xn < Yn < Zn} = 1 andXn p(d)→ Y, Zn p(d)→Y, then Yn p(d)→ Y. It is shown now that the stochastic ordering condition Xn - Y<p(d)→Yn - Y <d Xn - Y(Xn <dYn <d Zn) is a more general dominating condition than P{Xn < Yn < Zn} = 1 in ensuring the convergence in probability (in distribution) of {Yn}.
本文引入随机序(≤_d)的概念,说明在讨论随机变量列的依概率(依分布)收敛问题时,它是一个颇为恰当的“控制尺度”.
基金
This project is supported by the National Natural Science Foundation
