有关可交换随机变量序列的一个结论

A conclusion of exchangeable random variables

研究一定相关性条件下可交换随机变量与独立同分布随机变量的结果之间的相似与不同。利用逆鞅、截尾等方法,解决其渐近性质的问题。由于可交换随机变量的基本结构定理De Finetti定理——可交换随机变量无限序列以其尾σ-代数为条件是独立同分布的,因此可交换随机变量应该具有类似于独立同分布随机变量的性质。

In this paper, the similarity and difference of identically distributed random variables and exchangeable random variables sequences in certain relevant conditions are researched. This paper uses reverse martingale approach to solve the approximate behavior problems of finite exchangeable random variables se- quences. As the De Finetti＇s theorem states that infinite exchangeable random variables sequences is independent and identically distributed with the condition of the tailor - algebra. So some results about independent identically distributed random variables is similar to exchangeable random variables.