局部紧半群上概率测度组合收敛的某些结果

本文讨论局部紧半群上概率测度的组合收敛性,主要结果是利用局部群化的方法给出了概率测度组合收敛的一些结果.     

关于广义齐次自相似集上Hausdorff测度的一个特征

设E是Hausdorff测度正有限的广义齐次自相似集,本文证明了s维Hausdorff测度是E上唯一的非扩张概率测度.     

关于广义齐次自相似集上Hausdorff测度的一个特征

设E是Hausdorff测度正有限的广义齐次自相似集,本文证明了s维Hausdorff测度是E上唯一的非扩张概率测度.     

直觉模糊事件概率测度熵

针对模糊熵对不确定系统描述的缺陷,引入直觉模糊事件及其概率测度的概念,并给出了直觉模糊子集概率测度熵的定义,运用直觉模糊事件及其概率测度的基本性质,推导出了直觉模糊概率测度熵的一些基本定理,为不确定信息的描述和处理提供新的思路.     

随机整数划分的概率分析（英文）

令n≥1是自然数,它的一个整数划分是一列自然数λ_1,λ_2,…,λ_l(l≥1)使得λ_1+λ_2+…+λ_l=n.令P_n表示n的所有整数划分的集合,P表示所有整数划分的集合,通过赋予每个划分λ一个概率测度可以得到概率空间.特别地,有趣的概率测度包括均匀测度和Plancherel测度以及乘性测度.这些整数随机划分的概率极限理论内容非常丰富.本文综述一些研究成果和进展,包括极限形以及波动.为叙述简单起见,主要集中在均匀划分和Plancherel划分,并且重点介绍两个模型中所用到条件概率的论证思想和方法,大多结果不加以详细证明.     

广义质心体的非对称版本（英文）

广义质心体是关于概率测度的Orlicz质心体的多元情形.考虑广义质心体的非对称版本,即将关于概率测度的非对称Orlicz质心体推广到多元情形,并建立相应的质心不等式.     

多叉树模型中鞅测度的刻画与构造

在无套利假设下,讨论了多叉树模型中鞅测度的构造问题.利用二叉树方法,构造了有限个符号测度.证明了-个概率测度为鞅测度的充要条件是它可以表示为这组符号测度的某个满足特定条件的凸线性组合.     

带随机移民分枝布朗运动在quenched概率下的中心极限定理（英文）

本文考虑当空间维数大于等于4时,带随机移民分枝布朗运动在quenched概率下的中心极限定理.与在annealed概率下的结果类似,极限是高斯随机测度;但当空间维数等于4时,高斯随机测度的协方差不同于annealed概率下的结果.     

可测函数序列关于弱收敛概率测度序列积分的极限定理

研究了可测函数序列关于弱收敛概率测度序列积分的极限定理及其控制收敛定理,并给出了概率测度弱收敛的若干新的等价条件.     

统计收敛的测度理论

建立统计收敛的测度理论已经成为统计收敛研究领域的核心问题, 因为一种合理的理论不仅是把各种统计收敛统一起来, 而且是统计收敛通向测度理论、积分理论、概率论和数理统计的桥梁. 基于这个原因, 首先 证明了由N 的所有子集生成的σ-代数$\mathscr{A}$ 上的所有有限可加概率测度的表示定理; 证明了每个有限可加概率测度都可以唯一的分解为一个可数可加概率测度和一个统计测度(即一个有限可加概率测度μ, 对任意的单 点集{k} 有μ(k)=0)的凸组合. 本文还证明了经典统计测度的许多良好性质, 例如: 由所有经典统计测度组成的集合$\mathscr{S}$ 在$\mathscr{A}$上赋予逐点收敛的拓扑就成为紧凸的~Hausdorff 空间; 每一个经典统计测度都是连续型的~(所以是缺原子的); 对N中的任意子集，每一类特殊的统计测度都满足互余极大极小原理; 每一类统计收敛都可以在统计测度的意义下得到统一.     

On the Distribution of the Extremes of Unequally Correlated Normal Variables with Applications to Antedependent Cluster Data

Based on a small correlations approach, this paper deals with the probability distributions of the order statistics under a general Gaussian model with unequal (positive or negative) correlations. Illustrations are given for the cluster data those follow suitable antedependence models.     

小麦茎秆与单穗重的相关性分析

主要是分析茎秆与单穗重和产量的相关性.以6个小麦品种为材料,分别测取了穗下茎长,茎粗,穗长,株高,节壁厚,节重及单穗重,对茎质与穗重进行了相关分析,结果表明:茎秆性状与穗重存在不同程度的相关性.其中,茎粗与单穗重呈正相关;节壁厚与单穗重呈正相关;节壁重与单穗重呈正相关;而株高和茎长与单穗重的关系不明显且较为复杂,应分情况讨论.     

A different construction of Gaussian fields from Markov chains: Dirichlet covariances

We study a class of Gaussian random fields with negative correlations. These fields are easy to simulate. They are defined in a natural way from a Markov chain that has the index space of the Gaussian field as its state space. In parallel with Dynkin's investigation of Gaussian fields having covariance given by the Green's function of a Markov process, we develop connections between the occupation times of the Markov chain and the prediction properties of the Gaussian field. Our interest in such fields was initiated by their appearance in random matrix theory.     

How to improve the performance of ATM multiplexers

We consider an ATM multiplexer with a finite or infinite buffer and stochastic output rate. There are independent, identical sources connected to this multiplexer which transmit fluid directly into the buffer. We show that the throughput of the multiplexer is increasing in the number of sources connected, where we scale the cell stream process in such a way that the mean and peak input rate stays unchanged. In the finite buffer case, the cell loss is decreasing in the number of sources connected. Hence more links improve the performance of ATM multiplexers. In the last part, we prove that correlations within cell stream processes have a negative effect on the performance of ATM multiplexers. These investigations provide easily computable lower bounds to performance measures.     

Expanding measures

We prove that any C1+α transformation, possibly with a (non-flat) critical or singular region, admits an invariant probability measure absolutely continuous with respect to any expanding measure whose Jacobian satisfies a mild distortion condition. This is an extension to arbitrary dimension of a famous theorem of Keller (1990) [33] for maps of the interval with negative Schwarzian derivative.Given a non-uniformly expanding set, we also show how to construct a Markov structure such that any invariant measure defined on this set can be lifted. We used these structure to study decay of correlations and others statistical properties for general expanding measures.     

A concept of negative dependence using stochastic ordering

A concept of negative dependence called negative dependence by stochastic ordering is introduced. This concept satisfies various closure properties. It is shown that three models for negetive dependence satisfy it and that it implies the basic negative orthant inequalities. This concept is also satisfied by the multinomial, multivariate hypergeometric. Dirichlet and Dirichlet compound multinomial distributions. Furthermore, the joint distribution of ranks of a sample and the multivariate normal with nonpositive pairwise correlations also satisfy this condition. The positive dependence analog of this condition is also studied.     

Remote control of quantum correlations in a two-qubit receiver by a three-qubit sender

We study remote control of quantum correlations (discord) in a subsystem of two qubits (receiver) via parameters of the initial state of another three-qubit subsystem (sender) connected to the receiver by an inhomogeneous spin s = 1/2 chain. We propose two parameters characterizing the creatable correlations. The first parameter is the discord between the receiver and the remainder of the spin s = 1/2 chain, and it concerns the mutual correlations between these two subsystems. The second parameter is the discord between the two nodes of the receiver and describes the inner correlations of the receiver. We study the dependence of these two discords on the inhomogeneity parameter of the spin chain.     

The super-efficiency procedure for outlier identification,not for ranking efficient units

In this paper, we conduct simulation experiments to evaluate the performance of two alternative uses of the super-efficiency procedure in Data Envelopment Analysis (DEA). The first is for outlier identification and the second is for ranking efficient units. We find that the ranking procedure does not perform satisfactorily. In fact, the correlations between the true efficiency and the estimated super-efficiency are negative for the subset of efficient observations, and the conventional DEA model performs as well as the super-efficiency DEA model when all observations are considered. However, when data are contaminated with outliers, the use of the super-efficiency model to identify and remove outliers results in more accurate efficiency estimates than those obtained from the conventional DEA estimation model.     

Quantum and classical correlations in high-temperature dynamics of two coupled large spins

We study the dynamical correlations between two coupled spins depending on time and the value of the spin quantum numbers. In the high-temperature approximation, we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations. We consider both orthogonal and nonorthogonal measurements in the basis of spin coherent states. We show that at small times, the quantum part of correlations becomes much less than the classical part as the spin quantum numbers increase, while the situation is quite different at times equal to half the quantum period.     

Some correlations in intersection-union tests and their relationship with complete power

We explore the relationship between some correlations and complete power in intersection-union tests. We invalidate the approach of using the product of individual powers from testing each individual hypothesis as a lower bound estimate of the complete power, assuming nonnegative correlations.