Precise asymptotic in the laws of large numbers and law of iterated logarithm for some statistics 一类统计量的强大数律和重对数律的精确极限性质
Law of the iterated logarithm of quantile density estimator for left truncated and right censored data 左截断右删失数据下分位密度估计的重对数律
The law of the iterated logarithm is a kind of profound result on the limit theory , it make the strong law of large numbers exact 重对数律是概率极限理论中一类极为深刻的结果，是强大数律的精确化。
This dissertation consists of five chapters , in which we discuss the complete convergence and the iterated logarithm under dependent random variables 本文分为五章，讨论了在相依变量的情形下的完全收敛性和重对数律。
In this paper , sufficient conditions are given for applicability of the law of the iterated logarithm for self - normalized sums of independent random vectors 摘要本文给出了独立随机向量序列自正则和的重对数律成立的一个充分条件。
As for pattern , the logarithmic formula is also effective either in core region or in surface layer , and the values of k in both cases become smaller but differ to each other 型分布则是指主流区仍可用对数公式表达，且k值变小；在近底区亦近似符合对数律，但两区的k值有所不同。
It is an extension of " the law of iterated logarithm of kolmogorov " . in the course of proving , we extend two lemmas and use the relating results of partial sum increment of independent r . v 本文主要讨论独立随机变量某种加权和重对数律，它是“ kolmogorov重对数律”的推广。在证明过程中，首先推广了两个引理，并用到了部分和增量的有关结果。
We have been familiar with " the law of iterated logarithm of kolmogorov " and " the law of iterated logarithm of hartman - wintner " . this paper will mainly discuss the law of iterated logarithm for some kind weighted partial sum 各种文献中对独立随机变量序列重对数律已有深入讨论，我们已熟知“ kolmogorov重对数律”及“ hartman - wintner重对数律” 。
By employing de finetti theorem , in chapter two we discuss the limit behaviour of interchangeable random variables squences , mainly including the convergence rates in the central limit theorem and the law of the iterated logarithm 第二章主要讨论了可交换随机变量序列的极限性质，具体包括中心极限定理的收敛速度和重对数律，所得的结论补充了可交换随机变量极限理论方面的结果。
As for i . i . d . r . v . , we get the extension of " the law of iterated logarithm of hartman - wintner " under weaker conditions . at the end of this paper , we discuss that the moment conditions of theorem are necessary to the law of iterated logarithm of this form 对独立同分布的情形，在更弱的条件下得到“ hartmnan - wintner重对数律”的推广，并在文章最后证明了此时对这种形式的重对数律定理中矩条件是必要的。
