摘要
本文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,得到任意二值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.证明的基本思想是构造带参数的滑动似然比,然后运用分析方法.同时推广了若干经典的结论作为本文的推论.
This paper introduces the notion of the asymptotic logarithmic moving likelihood ratio,as a random measure of the deviation between the joint distribution of the arbitrarily dependent random sequences and the product of the reference.By restricting the asymptotic logarithmic moving likelihood ratio,a subset of the sample space is given.In this subset,a kind of strong limit theorems represented by inequalities are obtained for the moving average of the partial sums of two-valued random sequences.The main idea of the proof is to construct a moving likelihood ratio with a parameter and apply the pure analytical method.As the corollaries,some classical results are generalized.
出处
《工程数学学报》
CSCD
北大核心
2011年第5期702-706,共5页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(11071104)
安徽省教育厅科研基金(2006Kj064B)~~
关键词
二值随机序列
滑动平均
渐近对数滑动似然比
强偏差定理
two-valued random sequences
moving average
moving likelihood ratio
strong deviation theorem
