关于随机受控随机序列滑动平均的若干强偏差定理

Some Strong Deviation Theorems for Moving Average of Stochastically Dominated Random Sequence

引入渐近对数滑动似然比作为任意相依随机序列联合分布与参考乘积分布的偏差的一种随机性度量,通过限制渐近对数滑动似然比给出样本空间的一个子集,在此子集上,得到随机受控的随机序列部分和滑动平均的一类用不等式表示的强极限定理,即强偏差定理。

In this paper, we introduce the asymptotic logarithmic moving likelihood ratio as a random measure between the joint distribution of arbitrarily dependent random variables and the product of reference distribution. By restricting the asymptotic logarithmic moving likelihood ratio, a subset of sample space is given. On the set, some strong deviation theorems for moving average of partial sums of stochastically dominated random variables, which represented by inequalities, i.e., the strong limit theorems, are obtained.