随机变量的截尾与几个经典强大数定律的推广

Truncations of Random Variables and Generalization of Some Classical Strong Laws of Large Numbers

利用随机变量的截尾方法和条件三级数定理这一工具研究任意随机变量序列的性质,得到了矩条件下任意随机变量序列的一类强极限定理和强大数定律以及一些简单实用的结论,推广了与此相应的一些结果和若干经典的强大数定律.

By use of truncation methods of random variables and conditional three series theorem, the properties of sequence of arbitrary random variables are discussed, a class of strong limit theorems and strong laws of large numbers for sequences of arbitrary random variables and some simply practical conclusions are obtained under moment conditions, and some conclusions corresponded with these and some classical strong laws of large numbers are generalized.