随机变量的截尾与任意随机变量序列的强极限定理

利用随机变量的截尾研究任意随机变量序列的性质,建立了一类矩条件下任意随机变量序列的强极限定理.作为推论,得到了可列非齐次马尔可夫过程的一个强极限定理,推广了鞅差序列当1≤p≤2和p≥2时的Chow定理,相应的一些已有结果和若干经典的关于独立随机变量序列的强大数定律是本文的特例。

Truncation of Random Variables and Strong Limit Theorems for Sequences of Arbitrary Random Variables

By use of truncation of random variables,the properties of sequences of arbitrary random variables are studied and a class of strong limit theorems for sequences of arbitrary random variables are discussed under moment conditions.As corollaries,strong limit theorems for countable nonhomogeneous Markov chains are obtained,Y.S.Chow theorem for martingale difference sequence when 1≤p≤2 and p≥2 are generalized and some conclusions corresponded with these and some classical strong laws of large numbers for the sequence of independent random variables are the particular cases of the result of this paper.