一类随机偏差定理与母函数方法

本文利用对数似然比的概念研究非负整数值随机变量序列的极限性质,得到一类随机偏差定理,即用不等式表示的一类强极限定理,其偏差界依赖于样本点．证明中提出了将母函数的工具应用于强极限定理研究的一种途径．     

关于可列非齐次马氏泛函的一类强偏差定理

本文利用关于{σn(ω),n≥0)的样本相对熵率的概念,研究相依离散型随机变量序列函数的极限性质,从而建立了一类关于可列非齐次马氏泛函的强偏差定理.     

关于随机选择系统的一类强偏差定理

本文将随机选择系统(或称为赌博系统)和对数似然比的概念引入非负整值随机变量序列的极限性质的研究,建立了一类关于随机选择系统的选择子序列的强偏差定理.     

任意随机组列的强极限定理

本文研究了任意随机组列的极限性质.利用构造鞅的方法得到了任意随机组列的强极限定理,所得结果摊广了任意随机适应序列和树上非齐次马氏链的强极限定理.     

任意随机变量序列关于随机选择的一类强偏差定理

本文通过引进极限相对对数似然比,利用限制似然比给出了样本空间的一个子集,得到了任意实值随机变量序列关于随机选择的一类用不等式表示的强极限定理.并作为推论得到了任意整值随机变量序列的m元序组的强偏差定理.     

马氏链集间转移的一类强大数定律

本文研究了马氏链从一个状态子集到另一个状态子集的转移概率的极限性质.利用Doob鞅收敛定理,获得了任意随机序列的强大数定律、马氏链泛函的强大数定律和强遍历定理.推广了马氏链传统转移概率的极限性质和强极限定理.     

关于任意随机变量序列泛函的一类强偏差定理

通过概率空间上的任意随机变量的分布与独立分布的比较.研究任意随机变量序列泛函的强偏差定理,即小偏差定理.将已有的某些连续型及离散随机变量序列的强偏差定理加以推广.     

无限随机赌金系统下手续费收取的合理性

利用上鞅的性质,讨论赌博中赌徒的随机选择系统(赌金)在[0,∞)上取值时,赌徒对随机变量序列的估计分布与真实分布之间的极限关系,得到了用不等式表示的强偏差定理,从而得到在随机变量独立情况下庄家合理收取入场费的条件.     

极限相对对数似然比与一类强偏差定理

本文引进极限相对对数似然比γ（ω）的概念，并利用它来研究相依离散随机变量序列的极限性质。得到了一类用不等式表示的强极限定理，本文称之为强偏差定理，其偏差界依赖于γ（ω）。     

关于相依离散随机序列的若干强偏差定理

首次引入随机序列滑动似然比与滑动相对熵概念作为刻画任意相依随机序列的独立逼近的随机性度量,利用B-C引理与分析方法相结合,研究任意离散随机序列部分和滑动平均的强偏差定理.作为推论,得到了关于广义经验分布函数的一个极限定理.最后,给出了若干例子.     

Some conditional results for conditionally strong mixing sequences of random variables

The relation between strong mixing and conditionally strong mixing is answered by examples, that is, the strong mixing property of random variables does not imply the conditionally strong mixing property, and the opposite implication is also not true. Some equivalent definitions and basic properties of conditional strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under non-conditional case.     

关于公平赌博的一个强极限定理

本文就较一般的情况引进公平赌博的概念,将关于Bernoulli序列赌博策略的一个强极限定理推广到取有限个值的相依变量的情况,并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.证明中提出了将测度的网微分法和条件母函数的工具应用于赌博系统强极限定理的研究的一种途径.     

任意B值随机变量序列关于条件期望的一类强极限定理

利用随机变量的截尾方法和条件三级数定理,研究任意B值随机变量序列的极限性质,得到了一类关于条件期望的强极限定理和鞅差序列收敛定理,推广了与此相应的一些结果和若干经典的强大数定律.     

A strong limit theorem on gambling systems

A strong limit theorem on gambling system for Bernoulli sequences is extended to the sequences of arbitrary discrete random variables by using the conditional probabilities. Furthermore, by allowing the selection function to take values in an interval, the conception of random selection is generalized. In the proof an approach of applying the differentiation of measure on a net to the investigation of the strong limit theorem is proposed.     

Conditional independence,conditional mixing and conditional association

Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional version of the strong law of large numbers for conditionally independent random variables and a conditional version of the Kolmogorov’s strong law of large numbers for conditionally independent random variables with identical conditional distributions are obtained. The notions of conditional strong mixing and conditional association for a sequence of random variables are introduced. Some covariance inequalities and a central limit theorem for such sequences are mentioned.     

Large Deviation Theorems for Gaussian Processes and Their Applications in Information Theory

We discuss on the large deviation theorems for stationary Gaussian processes and their applications in information theory. The topics investigated here include error probability of string matching, error probabilities for random codings, and a conditional limit theorem which justifies the maximum entropy principle.     

Conditional versions of limit theorems for conditionally associated random variables

Relation between association and conditional association is answered, several examples show that the association of random variables does not imply the conditional association, and vice versa. Several fundamental properties of conditional associated random variables are developed, which extend the corresponding ones under the non-conditioning setup. By means of these properties, some conditional Hájek-Rényi type inequalities, a conditional strong law of large numbers and a conditional central limit theorem stated in terms of conditional characteristic functions are established, which are conditional versions of the earlier results for associated random variables, respectively. In addition, some lemmas in the context are of independent interest.     

非负整值随机变量序列的一类强偏差定理

设是在中取值的一列随机变量，其联合分布为是S上的一个分布，该文研究对数似然比与之间的若干极限关系，得到了一类用不等式表示的强极限定理（称之为强偏差定理），其偏差界依赖于样本点．证明中结合区间刻分法，提出了将母函数的工具应用于强极限定理研究的一种途径．     

矩条件下的任意随机变量序列的一类强极限定理

本文利用随机变量的截尾方法和条件三级数定理,研究了任意随机变量序列在矩条件下的一类强极限定理,改进了与此相应的一些结果的条件.     

关于离散信源的若干强极限定理

本文研究了离散信源广义熵定理以及随机条件概率的广义调和平均a.s.收敛性,在证明中提出了将Markov不等式、Borel-Cantelli引理和随机条件矩母函数等工具应用于强极限定理的研究的一种途径.