随机独立

We give several sufficient conditions of NA and NSD properties of random variables, compare the closeness of distribution functions of order statistics between NA and independent rv's, investigate properties of NSD defined by supermodular functions, study the dependence structure of stationary Markov process and order statistics and their spacings from two samples, establish stochastic comparisons of order statistics of heterogeneous rv's in the hazard rate and the reversed hazard rate orders, and give the first analytic proof of the closure property of the up shifted likelihood ratio order under convolution.

给出判定一组随机变量NA性质的几个充分条件，并给出NA和独立随机变量的次序统计量之间"贴近性"的比较，系统地研究基于特殊函数类所定义的NSD负相依概念，给出一些判别NSD性质的结构定理和一些有用概率不等式。系统研究平稳马氏过程的相依结构。研究两样本次序统计量及其问题隔的相依结构。在失效率、反向失效率序和似然序意义下给出非齐次随机变量次序统计量的比较。给出上漂移似然序卷积封闭性的第一个解析证明。

This project also obtained several limit theorems for some important dependent random variables and stochastic processes, such as the Strassen law of the iterated logarithm for negatively dependent random variables, strong limit theorems for mixing random vectors in Banach spaces, sample path properties for two-parameter fractional Wiener processes, and so on.

随机环境中的随机变量与随机过程的研究在国内外相当活跃，本项目主要研究它们的极限性质，着重研究了随机风景中随机变量与随机过程的极限性质，主要取得了以下几个结果：首先对简单对称的Kesten-Spitzer随机游动在低阶矩的条件下给出了强逼近，大大减弱了前人要求任意阶矩的条件，然后对独立风景中的一般随机变量给出了强逼近的一般性结果，由此导出在风景和随机变量都只具有低阶矩的条件下的独立但不同分布、混合相依变量的强逼近，在只有弱高于二阶矩的条件下得到了重相对数律和弱收敛；给出了连续时间参数的Brown风景中Brown运动和稳定风景中稳定过程的滞后增量和连续模等精确样本轨道性质；同时给出了一些重要的相依随机变量和过程的若干极限定理，如负相关随机变量的Strassen重对数律、抽象空间上混合相依变量的一些强极限定理成立的充分必要条件、两参数分数Wiener过程的样本轨道性质等。

Fri particular, the Wittmann-type strong law of larg numbers for independent random variables is generalized to the case of NA random variables. We also present the sufficient and necessary condition of the laws of logarithm, and we extend Teicher-type strong law of the large numbers for sequence of NA random variables. Some of the laws of iterated logarithm of Teicher-type, Egorov-type arid Wittmann-type for sequence of NA random variables are obtained. Then we investigate the rate3f ionvergcll( fbr series of NA randonl variables, we obtain soIne results fbr tl1e Iaws of theiterated logarithttl, the laws of logarithm and decreasing order fOr the tail sum.Risk itllttlysis tlleory is a sigIlifica11t part of insurance InatheInatics.

Wittmann（1985a）关于实独立随机变量列的结果，并给出了NA列强大数律成立的若干条件，特别建立了一般NA列对数律成立的充分必要条件，在二阶矩存在的条件下完整的解决了一般NA列对数律的问题，中文摘要2而已有的一些NA列对数律的结果可以由它推出，给出了NA列的Teiclier型强大数律，表明lbiChCI·（1979）给出的实独立随机变量列的强大数律可以减弱其条件等；建立厂不问分布NA列的Teicfl仪；Egorov，Petrov型有界重对数律，以及加权同分布NA列的有界重对数律，进一步推广了NA列的Kolmogory有界重对数律等，特别对NA列建立了Wittm洲型有界重对数律，而其证明方法与独立情形有很大不同，同时通过反例表明在与独立场合类似的条件下，独立列的Wittmann有界重对数律不能完美的推广到NA歹小惰形；最后研究了NA随机变量级数的收敛速度，给出了尾和下降的阶；尾和的有界重对数律，及尾和对数律成立的充要条件等，并通过反例说明 NA随机变量级数与独立随机变量级数在收敛速度方面存在的差异。

The notion of sample relative entropy , as a random measure of the deviation of a sequence of nonnegative continuous random sequence from independent random sequence with exponential distribution, is introduced.

利用样本相对熵作为一般非负连续型随机变量序列相对于服从指数分布的独立但不同分布随机变量序列偏差的一种随机性度量，运用鞅理论及分析方法，研究了一类随机变量序列加权和的用不等式表示的极限定理，即强偏差定

And then obtained under some conditions of probability are some sufficient conditions for moment complete convergence for independent non-identically distributed random elements in a separable Banach space which are stochastically bounded by a positive random variable.

文章在随机元序列随机有界于某非负随机变量的条件下，引入慢变化函数l和选定的函数类S，在一定的概率性条件下，得到B值独立不同分布随机元序列矩完全收敛性的充分条件，推广了有关文献的结果。

In the third part, we study an application of stereographic projection transformation in statistics, deriving Box-Muller formula (use two independent uniform random number to generate two independent standard normal random number) and spherical symmetric distribution (a product of a positive random variable and a random vector with uniform distribution) in multivariate statistical analysis.

第3章，研究了球极投影变换在统计中的应用，通过球极投影变换获得了利用两个相互独立的均匀随机数生成两个相互独立的标准正态随机数的Box-Muller公式以及多元统计分析中的球对称分布（一个正的随机变量和一个与之相互独立的均匀分布的随机向量的乘积）。

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。

Considering the spatial correlations of interconnect process variations, we modelprocess variations as continual stochastic processes with correlation. For decoupleing thespatial correlation, we express them as an expanded form of independent random variablesby Karhunen-Loeve expansion. Then we use stochastic Galerkin method to solve thedecoupled telegraph equation in the presence of process variations.

考虑互连线工艺变化的空间相关性，将互连线工艺变化建模为具有相关性的连续随机过程；提出采用Karhunen-Loeve展开将该随机过程表示为一组独立随机变量的展开式，从而进行解耦；对解耦后得到的工艺变化下的电报方程，应用随机迦辽金方法求解。

Based on the principle of energy equivalence, the expanding expression of seismic acceleration process is achieved. The seismic process is expanded into a linear combination of deterministic functions modulated by 10 uncorrelated random variables.

为此，提出了从地震动位移过程的正交展开出发，引入一类能量等效原理，获得了地震动加速度随机过程的正交展开式，进而将地震动随机过程展开为由10个独立随机变量所调制的确定性函数的线性组合形式。

The local averaging method is used to discretize the random field, correlated random variables are transformed to a set of uncorrelated normalized random variables, combining viscoelastic stochastic finite element method with H-L algorithm, the reliability of solid propellant grain is studied with different random parameters.

为了讨论各类随机因素对药柱结构可靠性的影响，采用局部平均法离散参数随机场，并通过相关结构分解成归一化的独立随机变量，将可靠度指标算法和粘弹性随机有限元法相结合，进行了固体推进剂药柱的结构可靠性分析。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。