导　　师： 张立新

学科专业： 070104

授予学位： 硕士

作　　者： ;

机构地区： 浙江大学

摘　　要： 自从1960年引入ρ—混合序列的概念和80年代提出了NA序列的概念以来，很多学者对它们的弱收敛，最大值不等式和完全收敛性进行了研究．至今有了很多结果，其中有关相依序列的许多结果是在独立序列的基础上推广得到的，本文尝试着在对它的部分和最大值的极限性质作进一步讨论． 第一章简要地介绍了NA相依序列和ρ—混合序列的定义和之前的主要结论．特别的，张立新/(2004/)得到了关于NA序列重对数律的几个极限定理；成凤肠，王岳宝/(2004/)给出了独立与NA列部分和的精致渐近性的一般形式；而赵月旭等/(2007/)提出了强平稳ρ—混合序列的精确渐近性． 第二章我们用张立新/(2004/)和成凤旸，王岳宝/(2004/)的方法得到了在NA序列下关于部分和最大值与重对数律和Chung对数律相关的精确渐近性的一般形式． 第三章我们用Huang W．et al．/(2003/)和赵月旭等/(2007/)的方法得到了在ρ—混合序列下关于部分和最大值与重对数律相关的精确渐近性的一般形式． The definition ofρ-mixing was advanced in 1960 and the definition of NA was in the 1980s. Form then on, many scholars have discussed their limit properties in weak convergence, maximal inequality and the complete convergence. There are many results now which are mostly derived from the i.i.d, sequences. In this paper I try to discuss its further limit properties in maximal partial sum. In chapter one, we introduce the definition ofρ-mixing sequence, NA/(negative association/)and the main results which were proved by the scholars before. Especially, Zhang L.X./(2004/)proved the complete convergence in NA sequences; Feng Y.C., Wang Y.B./(2004/) proved precise asymptotics of partial sums forⅡD and NA sequences; Zhao Y.X. et al. /(2007/)gives the precise rate in theρ-mixing sequeces. In chapter two we derive a general form of precise rate in the limit properties for maximal partial sum for NA sequences, by combining the methods in Zhang L.X. /(2004/)and Feng Y.C., Wang Y.B./(2004/). In chapter three we derive a general form of precise rate in the in the law of the iterated logarithm for maximal partial sum in theρ-mixing sequences, by combining the methods in Huang W. et al./(2003/) and Zhao Y.X. et al. /(2007/).

关 键 词： 序列 混合序列 部分和最大值 重对数律 对数律

分 类 号： [O211.5]

领　　域： [理学] [理学]