整值随机序列滑动平均的小偏差定理

Small Deviation Theorems for Moving Averages of Integer-valued Random Sequence

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Poisson分布的独立随机变量序列偏差的一种度量,通过滑动相对熵给出样本空间的一个子集,在此子集上得到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。

A moving likelihood ratio is employed as a metric of the deviation of a sequence of integer-valued random variables from independent random sequence with Poisson distribution. By restricting the moving relative entropy, a subset of the sample space is given, and on this subset, a class of strong limit theorems about moving average of random sequence,represented with inequalities, namely small deviation theorems, are obtained.