Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results

This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a recent strong law for Lz-mixingales, and also a new strong law for Lpmixingales. These results greatly relax the dependence and heterogeneity conditions relative to those currently cited, and introduce explicit trade-offs between dependence and heterogeneity. The results are applied to proving strong laws for near-epoch dependent functions of mixing processes. We contrast several methods for obtaining these results, including mapping directly to the mixingale properties, and applying a truncation argument.     

Strong convergence properties for partial sums of asymptotically negatively associated random vectors in Hilbert spaces

Abstract

In this paper, we investigate the almost sure convergence for partial sums of asymptotically negatively associated (ANA, for short) random vectors in Hilbert spaces. The Khintchine-Kolmogorov type convergence theorem, three series theorem and the Kolmogorov type strong law of large numbers for partial sums of ANA random vectors in Hilbert spaces are obtained. The results obtained in the paper generalize some corresponding ones for independent random vectors and negatively associated random vectors in Hilbert spaces.     

H公式与完全相关数对

定义完全相关数对并推导出求完全相关数对个数的H公式。     

On convergence rate in the SLLN for maximums of moving-average sums of ALNQD random fields

In this article, we define a notion of asymptotically linear negatively quadrant dependence and establish the rate of complete convergence for maximums of moving-average sums of asymptotically linear negatively quadrant dependent random fields.     

利用差分求Bernoulli数

本文利用组合数学中的差分方法对Bernoulli数求法进行研究。     

中西方数字文化观的比较与翻译

对中西方数字观异同表现及原因和英汉数词的模糊性进行了比较,并论述了数词翻译的原则与方法。     

温度的洛仑兹收缩

介绍理想气体系统中单粒子态平均占有数的普遍表达式，并根据此表达式导出两种惯性参照系中绝对温度Ｔ的洛仑兹收缩关系，由此提出摄氏温度ｔ的洛仑兹收缩关系的假设，再分别通过温度换算关系Ｔ＝Ｔ（ｔ）和平均占有数理论对推导加以证明。     

Laws of large numbers for bootstrappedU-statistics

For the bootstrapped mean, a strong law of large numbers is obtained under the assumption of finiteness of the rth moment, for some r>1, and a weak law of large numbers is obtained under the finiteness of the first moment. The results are then extended to bootstrapped U-statistics under parallel conditions. Stochastic convergence of the jackknifed estimator of the variance of a bootstrapped U-statistic is proved. The asymptotic normality of the bootstrapped pivot and the bias of the bootstrapped U-statistic are indicated.     

现代汉语数范畴说略

汉语的数范畴横跨词法和句法两大领域,并在表达中得以体现。其体系是以泛数和定数的对立为表现形式,以绝对的和相对的单复数为基础,以静态和动态为两大语用特点。汉语的数范畴体系体现了汉语在语言类型学中的个性化特点。     

古希腊筛法及其推广

由古希腊筛法推广出的XZG筛法引出相关数对,由素殆2相关数对推出完全相关数对.