关于整值随机序列滑动平均的若干小偏差定理

On Small Deviation Theorems for Moving Averages of Dependent Integer-Valued Random Sequence

本文引入随机序列滑动似然比作为任意整值随机序列相对于服从几何分布的独立随机变量序列偏差的一种度量,并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。

In this paper, the notion of moving likelihood ratio, as a measure of the deviation of a sequence of integer-valued random variables from an independent random sequence with geometric distribution, is intro-duced. By restricting the moving likelihood ratio, a certain subset of the sample space is given, and on this subset, a class of strong laws, represented by inequalities, are obtained. These strong laws contain some limit properties of the sequence of integer-valued random variables, concerning relative entropy density and the entropy function of geometric distribution.