They are extensions of the limit properties for nonhomogeneous markov chains , gambling systems , and the harmonic mean of random conditional probablities 它是非齐次马氏链、赌博系统、随机条件概率的调和平均等极限性质的推广。
Then an important property is obtained : when a - 0 , the first order derivative of the degree 3 c - b zier curve is that of the degree 3 bezier curve , aber the second order derivative of the degree 3 c - b zier curve has no the property Zier曲线导矢的一个极限性质：当0时，三次c - b ? zier曲线一阶导矢的极限为同次b ? zier曲线的一阶导矢，并指出了该极限性质对c - b
For any information source on a countable set , the limit properties of relative likelihood ratio and log - likelihood ratio of entropy with respect to the independent geometry distribution , an important problem in the information theory is discussed 摘要对任意的可列集上的信息源，探讨资讯论的一个重要问题，即探讨了相对于独立型几何分布的熵密度似然比与对数似然比的极限性质。
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。
Markov chains are special random process . renently , professor liu wen , who first invented the analysis method in solving large number theory , connected it and markov chains and got some limit properties about one - order markov chains 刘文教授在大数定律的研究中把首创的分析方法和马氏链结合起来，得出一系列有关一重马氏链的极限结果，本论文继续并拓广这方面的研究，相应于一重马氏链，二重马氏链也有其相应的极限性质。
By the asymptotic properties of random walk we develop suffcient conditions for the convergence of conditional solution to nonconditional solution , necessary and sufficient conditions for the finiteness of absolute moments of any order and for the persistence of endogenous variables and exogenous variables 利用随机游动的极限性质得到了条件解收敛于无条件解的充分条件，任意阶矩有限的充要条件以及外生变量与内生变量持续性的充要条件。
In chapter l , we introduce the relative background on this paper and give some simple expressions of the work which have been studied . in chapter 2 , in virtue of the notion of likelihood ratio the limit properties of the sequences of dependent nonnegative continuous random variables are studied , and a class of strong limit theorems represented by inequalities are obtained . the bounds given by these theorems depend on positive constant c . in chapter 3 , by means of the notion of log likelihood ratio , a kind random strong deviation theorem are obtained , and the bounds given by these theorems depend on r ( ) 第一章，介绍本论文的选题背景，对已有的工作进行扼要的介绍；第二章，利用似然比的概念研究相依连续型非负随机变量序列的极限性质，得到一类强偏差定理，其偏差界依赖于正常数c ；第三章，利用对数似然比的概念得到一类随机偏差定理，其偏差界依赖于r ( ) ，证明中引进了尾概率和尾概率的laplace变换的概念；第四章，利用对数似然比的概念，得到了一类关于任意连续型随机变量序列的泛函的强偏差定理。
In chapter one , we discuss the limit behaviour of a kind of symmetric random variables sequences , mainly including the strong law of large numbers , the convergence rates of tail probabilities in the law of large numbers and the convergence rates of tail probabilities in the law of large numbers with random index . the results obtained extand some results of classical limit theory under the independent situation 第一章主要讨论了一类分布对称随机变量序列的极限性质，具体包括强大数定律、大数律尾概率级数的收敛性以及具有随机足标的大数律尾概率级数的收敛性，从而对独立情形下的经典极限理论部分结果进行了条件的推广。
In this paper , by means of the notion of likelihood ratio and log likelihood ratio the limit properties of the sequences of dependent continuous random variables are studied , and a class of strong limit theorems represented by inequalities are obtained . in the proof an approach of applying the tool of laplace transform to the study of strong limit theorem is proposed 本论文继续这方面的工作，利用似然比、对数似然比的概念研究相依连续型随机变量序列的极限性质，得到相应的用不等式表示的强偏差定理。证明中提出了将laplace变换的工具应用于强极限定理研究的一种方法。
Our results show that the rate of correlation among the random variables of those output sequences are low although they are not independent ; in addition , the output sequences of those combined generators are homogeneous markov chains which are strictly stationary processes with ergodicity ; the output sequences of those combined generators are also proved to summit to the strong law of large numbers and the central limit theorem ; finally the computation formula of the rate of the accordance between the output sequences and input sequences of those combined generators is given 我们的研究结论表明：虽然这些序列中随机变量之间不具有相互独立性，但它们的相关程度却比较低；证明了“停走”生成器， km _ 1m _ 2型组合生成器和加法型组合生成器的概率模型输出序列都是强平稳的和遍历的齐次马氏链；讨论了这些序列的概率极限性质，证明了它们均服从强大数定律和中心极限定理；还分别给出了各类生成器的输出序列与输入序列之间的符合率的计算公式。
