Lil is a very precise phenomena whose rates of convergence have attracted many scholars " attention . [ 7 ] and [ 8 ] discussed the rate of convergence in lil of i . i . d . random sequences ; [ 9 ] discussed the convergence rates in the law of logarithm of na sequences [ v ] ， [ s ]研究了独立同分布随机变量序列重对数律的收敛速度; [ 0l研究了na随机变量序列的对数律的收敛速度; 14 ]研究了b值独立同分布随机变量的收敛速度;
The paper consists of two chapters . in the first chapter , theory 1 [ 1 ] mainly by using the method of the law of the iterated logarithm with finite partial sum in wiener process proves hartman - wintner [ 1 ] law of the iterated logarithm for special finite partial weight sums 本文正文分两部分，定理1主要利用[ 1 ] wiener过程下的有限项部分和的重对数律，把hartman - wintner重对数律[ 1 ]推广到对特殊加权部分和也成立。
The limit theory of law of the iterated logarithm have received more and more attentions , especially about identical independent random variables . but up to now , the studies are only for partial sums and , have n ' t shown any concern on the special finite partial weight suras . however , the partial sums and partial weight sums not only have the osculating aspects , but also have essential difference between them . so the studies for these play an important role in theoretical and applied setups 因此对重对数律的研究引起了国内外学者的兴趣，对独立同分布的随机变量，许多学者做了大量的研究工作，但迄今为止这方面的研究仍限于部分和数列的重对数律，很少涉及到特殊加权和的领域，而部分和与加权和之间既有密切联系，又有本质不同，因此，这一问题的研究具有一定理论意义和应用价值。
A kind of complete convergence of sums for negatively associated sequences of non - identically distributed random variables , in the second chapter , is obtained and the requirement of known results are weakened to the condition that absoluted moment - larger than zero - is finite . the strong convergence of negatively associated sequences of non - identically distributed random variables is discussed in the third chapter . in the fourth chapter , after extend the laws of the iterated logarithm of strong stationary case to weak stationary case , we obtain the strong convergence rate for negatively associated sequences of non - identically distributed random variables in linear models 其中第二章讨论了一类不同分布的na列的加权和的完全收敛性，我们把已有的结果对矩的要求放宽到了只要求大于0的绝对矩有限的情形；第三章讨论了不同分布的na列的加权和的强收敛性；第四章首先把文[ 10 ]的关于na的重对数律由强平稳的情形推广到了弱平稳不同分布的情形，然后得到了线性模型中不同分布的na误差列的收敛速度。
Let { xn ; n > 1 } be mutually identically independent random variables distributed according to the normal distribution , { sn , n > 1 } be finite partial sum series , the purpose of this paper is to investigate law of the iterated logarithm type results for special finite partial weight sum series { sn , n > 1 } , we assume that sn = a1sn + a2 ( s2n - sn ) + a3 ( s3n - s2n ) + . . . + ad ( sdn - s ( d - 1 ) n ) in the second chapter , theory 2 by using the method of literature [ 8 ] , we extend hartman - wintner law of iterated logarithm on the gauss distribution . we substitute negative correspond for independent . it extends the corresponding results in gauss distribution 设{ x _ n ； n 1 }是独立同分布的且服从标准正态分布的随机变量序列， { s _ n , n 1 }是其部分和数列，讨论有限项特殊加权部分和{ s _ n ， n 1 }的重对数律，其中定理2利用文献[ 8 ]提供的方法，在高斯分布上改进了hartman - wintner的重对数律，取消独立性用更弱的条件负相关代替，大大拓宽了重对数律在高斯分布中的使用范围。
