随机相依

The purpose of this project is to study the theory of statistical dependence and stochastic comparisons with their applications in actuarial science.

本项目旨在研究统计相依与随机比较的基本理论及其在精算学中的应用。

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。

To describe the asymptotic behavior of certain time series or random fields,many ways of modeling the weak dependence have already been work out.

为了描述某些时间序列和随机场的渐近行为，许多作者引入了随机变量的相依性概念，其中最流行的就是混合概念。

Using copula for measuring dependence takes more attentions in recent years.

近些年来利用copula刻画随机变量间相依性的理论越来越受到人们的关注。

For example, Burton and Dehling (1990) have obtained a large deviation principle for the linear processes, Yang (1996) has established CLT and the law of the iterated logarithm, Li et al.

其实，关于相依随机变量的极限性质的研究可以追溯到二十世纪二、三十年代，当时就有Bernstein(1927)、Hopf(1937)和Robbins(1948)等学者相继对其进行研究。

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。

Stationary NA sequences; empirical measure; large deviations principle; linear processes; functional law of the iterated logarithm; strong approximations; LPQD sequences; m-dependent random element; precise asymptotics; the central limit theorem for the sum of random number

基础科学，数学，概率论、数理统计平稳NA序列；经验测度；大偏差原理；线性过程；泛函型重对数律；强逼近； LPQD序列； m-相依随机元；精确渐近性；随机指标中心极限定理

A strong limit theorem on gambling strategy for Bernoulli sequences is extended to the sequences of arbitrary dependent random variables which take numberable values by using the conditional moment generating function .

利用条件矩母函数将关于Bernoulli序列赌博策略的一个强极限定理推广到取可列值的任意相依随机变量序列的情况，并且通过允许选择函数在一个区间中取值，推广了随机选择的概念。

Secondly, we obtain the moderate deviation principles for NA random variables with stationary distribution under a weak condition, and then we give the MDP for m-dependent random variables..

其次， 我们在一比较弱的条件下得到了平稳NA随机变量列的中偏差原理，并给出了m相依随机变量列的中偏差原理。

The vertex set denotes random variables at different times, and the directed edges denote causal dependence between the variables.

定义了线性条件互信息图，图中的结点表示时间序列不同时刻的随机变量，结点间的边表示随机变量之间存在的因果相依关系。

Kate: I'm sorry I kissed you.

抱歉，我亲了你。

This means giant network to buy long swim the hearsay of the net is complete by checkmate.

这意味着巨人网络收购久游网的传闻彻底被击破。