极限定理

We give some results on the strong law of large numbers for sequence of negatively associated random variables with different distributions.

给出了具有不同分布的NA随机变量列满足的若干强大数律；作为应用，不仅将独立随机变量的一类强极限定理完整的推广到NA随机变量情形，而且关于NA随机变量的一些已有结果可以作为推论得出。

Thirdly, proper probabilistic model is built for the bilateral stop-and-go generator and the probability properties of its output sequence are studied. It is proved that the output sequence obey strong law of large numbers and central limit theorem and that, however, the distributions of 0 and 1 in the output sequence are imbalanced, which implies that this generator cannot be used as keystream generator directly. The rate of coincidence between the output sequence and corresponding LFSR sequences, together with their first derivatives are obtained, which reveal the existence of correlation between these sequences.

最后，建立了双侧停走生成器的概率模型，研究了双侧停走生成器输出序列的概率分布性质和大数性质，证明了生成器输出序列服从强大数定律和中心极限定理，得到了生成器输出序列中0，1分布是不平衡的结论，由此指出不能将这种生成器直接作为密钥流生成器；给出了双侧停走生成器输出序列和相应的线性移位寄存器序列之间的符合率以及一阶差分序列之间的符合率，得到了符合率的表达式，揭示了这些序列的对应比特和对应序列段之间存在相关性。

Secondly, the properties of output sequences of stop-and-go clocked combiners are discussed. It is proved that the output sequences are stationary and obey strong law of large numbers and central limit theorem. Using the probabilistic model properly built, we analyze the rate of coincidence between the output sequences of two kinds of generators with basic operations and corresponding LFSRs sequences. All the computational formulae are derived. A recursive algorithm for efficiently computing the poster probability of partial input strings and corresponding joint probability is introduced. Moreover, divide-and-conquer attacks on this kind of generators which reconstruct the initial states of the input stop-and-go generators individually are proposed.

其次，分析了一般钟控停走组合生成器输出序列的概率分布性质，证明了生成器的输出序列是严平稳的，且服从强大数定律和中心极限定理；考察了钟控加法型组合生成器和钟控乘法型组合生成器的输出序列和相应的常规钟控下线性移位寄存器序列之间的符合率，给出了符合率的具体计算公式；给出了组合器输出序列段和输入序列段之间的联合分布以及部分输入序列段的后验概率的有效递归算法，进一步提出了利用后验概率对钟控组合生成器进行分别征服相关攻击的方法。

A strong ilmit theorem for the weighted sum of discrete random sequences is gotten by the method of net differentiability.

文摘：利用网微分法，给出了离散型随机变量序列加权和的一个极限定理。

In this paper,we mainly make a deep and systematic study of sample path prop-erties for high and infinite dimensional Gaussian processes,especially for high andinfinite dimensional Wiener process in stronger norm-Holder norm than ever(everbefore,there used to be uniform norm and the process was limited to one dimen-sion).We not only deal with all kinds of functional moduli of continuity,but alsoconcern with different forms of functional limit theorems of C-R increments.

本文主要对高维的以至无穷维的Gauss过程、特别是Wiener过程的样本轨道性质在较以往更强的范数—〓范数下作了系统深入的研究（以往通常采用一致范数，过程限于一维），研究的内容不仅包括各种形式的泛函连续模，而且还包括各种形式的C-R增量的泛函极限定理。

This paper introduced the appliance of probability and statistics in reality,including classical model,formula of total probability, normal distribute,mathematics expectation and the central limit theorem.While it also discusses the widely uses of probability and statistics and the close relationship with the real life.Therefore,it lays the theoretical foundation for the practical uses with probability and statistics,and the basis of mathematics model.

本文介绍了概率统计的某些知识在实际问题中的应用，主要围绕古典概型，全概率公式，正态分布，数学期望，极限定理等有关知识，探讨概率统计知识在实际生活中的广泛应用，进一步揭示概率统计与实际生活的密切联系，为应用概率知识解决实际问题，数学模型的建立，学科知识的迁移奠定一定的理论基础。

Major topics covered are: basic concepts of probability, sample space and events, axioms of probability, random variables, discrete and continuous distributions, joint and marginal distributions, numerical characteristic for random variables, the weak law of large numbers, central limit theorem, basic concepts of statistics, parameter estimate, hypothesis testing and regression analysis.

本课程的基本内容有：随机事件及其概率、随机变量及其分布、多维随机变量及其分布、随机变量的数字特征、大数定律与极限定理、数理统计的基础知识、参数估计、假设检验、回归分析。

Comparing with the indexes of PR and PRE priority discipline queuing systems with service interruptions, we obtain some weak limit theorems for the workload and queuing length processes.

通过对比PR优先原则下和PRE优先原则下的服务中断排队系统的相应指标，获得了负荷和队长过程的弱极限定理。

Using the research results of Wiener process and limited fraction Theory, researched on the distribution of inspecting statistic, which lies in the non-stationary process.

利用维那过程的研究成果及泛函中心极限定理对非平稳过程的检验统计量分布进行了研究。

The analytic technique which is first invented by professor Liu Wen is skillfully introduced to the study of strong limit theorems for Markov chain fields on trees by professor Liu Wen and his copartners. In this paper, the martingale technique is applied to continue the study in this respect.

刘文教授及其合作者把刘老师首创的分析方法巧妙的引入了树上马尔可夫链场的强极限定理的研究工作中，本论文应用鞅方法继续了这方面的研究工作。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。