相依随机序列加权和滑动平均的若干小偏差定理

On Small Deviation Theorems of Moving Averages of Weighted Sums for Dependent Stochastic Sequence

引入随机序列滑动似然比作为任意二值随机序列相对于Bernoulli分布的独立随机变量序列偏差的一种随机性度量,通过滑动相对熵给出了样本空间的一个子集.在此子集上得到了一类关于随机序列滑动平均的用不等式表示的强极限定理,即小偏差定理,推广了文献[5],[6]等关于随机序列算术平均的结果,这些结果蕴含近期诸多文献的主要结果.

The notion of moving likelihood ratio, as a measure of the deviation of a sequence of two-valued random variables from an independent random sequence with Bernoulli distribution, is introduced. By restricting the moving likelihood ratio,a certain subset of the sample space is given,and on this subset, a class of strong taws, represented by inequalities,are obtained, which extend the results of Liu and Wang on arithmatic average. These conclusions include some results of the recent paper.