Complete moment convergence for ND random variables under the sub-linear expectations

In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of results on complete moment convergence for ND random variables under the sub-linear expectations.

STRONG LIMIT THEOREMS FOR EXTENDED INDEPENDENT RANDOM VARIABLES AND EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have attracted a lot of interest recently.The purpose of this paper is to study the strong law of large numbers and the law of the iterated logarithm for a sequence of random variables in a sub-linear expectation space under a concept of extended independence which is much weaker and easier to verify than the independence proposed by Peng[20].We introduce a concept of extended negative dependence which is an extension of the kind of weak independence and the extended negative independence relative to classical probability that has appeared in the recent literature.Powerful tools such as moment inequality and Kolmogorov’s exponential inequality are established for these kinds of extended negatively independent random variables,and these tools improve a lot upon those of Chen,Chen and Ng[1].The strong law of large numbers and the law of iterated logarithm are also obtained by applying these inequalities.

Central limit theolrem for linear processes generated byⅡD random variables under the sub-linear expectation

In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expectations initiated by Peng[19].It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive.

Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations

In this article,we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.We establish general strong law and complete convergence theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.Our results of strong limit theorems are more general than some related results previously obtained by Thrum(1987),Li et al.(1995)and Wu(2010)in classical probability space.

The Sufficient and Necessary Conditions of the Strong Law of Large Numbers under Sub-linear Expectations

In this paper, by establishing a Borel–Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random variables on R^(∞) under a probability, we give the sufficient and necessary conditions of the strong law of large numbers for independent and identically distributed random variables under the sub-linear expectation, and the sufficient and necessary conditions for the convergence of an infinite series of independent random variables, without the assumption on the continuity of the capacities. A purely probabilistic proof of a weak law of large numbers is also given.

Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications

In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz's strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive.

Donsker’s Invariance Principle Under the Sub-linear Expectation with an Application to Chung’s Law of the Iterated Logarithm

We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.

The Convergence of the Sums of Independent Random Variables Under the Sub-linear Expectations

Let {Xn;n≥1} be a sequence of independent random variables on a probability space(Ω,F,P) and Sn=∑k=1n Xk.It is well-known that the almost sure convergence,the convergence in probability and the convergence in distribution of Sn are equivalent.In this paper,we prove similar results for the independent random variables under the sub-linear expectations,and give a group of sufficient and necessary conditions for these convergence.For proving the results,the Levy and Kolmogorov maximal inequalities for independent random variables under the sub-linear expectation are established.As an application of the maximal inequalities,the sufficient and necessary conditions for the central limit theorem of independent and identically distributed random variables are also obtained.

次线性期望空间下独立同分布序列的一个强大数定律

利用与概率空间不同的研究方法,研究次线性期望空间中独立同分布随机变量序列的加权和在某些条件下的一个强大数定律,从而将该定理从传统概率空间扩展到次线性期望空间.

Lindeberg's central limit theorems for martingale-like sequences under sub-linear expectations

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.

On the laws of the iterated logarithm under sub-linear expectations

In this paper,we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space,where the random variables are not necessarily identically distributed.Exponential inequalities for the maximum sum of independent random variables and Kolmogorov’s converse exponential inequalities are established as tools for showing the law of the iterated logarithm.As an application,the sufficient and necessary conditions of the law of the iterated logarithm for independent and identically distributed random variables under the sub-linear expectation are obtained.In the paper,it is also shown that if the sub-linear expectation space is rich enough,it will have no continuous capacity.The laws of the iterated logarithm are established without the assumption on the continuity of capacities.

一种基于加权拟合的定制家居封边板材尺寸测量方法

板材在流程化加工过程中,会因为辊道的不连续性导致其在运动过程中震动和倾斜,给其尺寸的在线测量带来困难。根据板材的形状特点,提出一种基于加权灰度矩的亚像素边界拟合定位方法,以实现宽度的准确测量。首先利用方向滤波和边缘算子进行边缘筛选,利用最小二乘法拟合边缘点集合得到像素级边缘,再基于离群度的灰度矩加权拟合方法,定位得出板材边缘的亚像素位置,克服了震动和光照造成的边缘离散问题,同时结合线阵相机的单维度标定方法,获得了板材宽度的测量结果。现场测试表明,该方法的测量精度小于0.1 mm,满足工厂测量的要求,且具有较好的鲁棒性。

次线性期望下宽相依随机变量的完全f-矩收敛性

基于次线性期望下宽相依(WOD)随机变量的完全f-矩收敛性,强调了WOD随机变量在解决实际问题中的重要性。与完全矩收敛相比,完全f-矩收敛具有更强的性质。通过引入次线性期望的概念,运用了次线性期望空间下的一系列性质,结合新的容度不等式及证明方法,将完全f-矩收敛定理从传统的经典概率空间推广到了更为广阔的次线性期望空间。

基于局部Transformer的泰语分词和词性标注联合模型

泰语分词和词性标注任务二者之间存在高关联性,已有研究表明将分词和词性标注任务进行联合学习可以有效提升模型性能,为此,提出了一种针对泰语拼写和构词特点的分词和词性标注联合模型。针对泰语中字符构成音节,音节组成词语的特点,采用局部Transformer网络从音节序列中学习分词特征;考虑到词根和词缀等音节与词性的关联,将用于分词的音节特征融入词语序列特征,缓解未知词的词性标注特征缺失问题。在此基础上,模型采用线性分类层预测分词标签,采用线性条件随机场建模词性序列的依赖关系。在泰语数据集LST20上的试验结果表明,模型分词F1、词性标注微平均F1和宏平均F1分别达到96.33%、97.06%和85.98%,相较基线模型分别提升了0.33%、0.44%和0.12%。

The Law of Logarithm for Arrays of Random Variables under Sub-linear Expectations

Under the framework of sub-linear expectation initiated by Peng,motivated by the concept of extended negative dependence,we establish a law of logarithm for arrays of row-wise extended negatively dependent random variables under weak conditions.Besides,the law of logarithm for independent and identically distributed arrays is derived more precisely and the sufficient and necessary conditions for the law of logarithm are obtained.

The laws of large numbers for Pareto-type random variables under sub-linear expectation

In this paper,some laws of large numbers are established for random variables that satisfy the Pareto distribution,so that the relevant conclusions in the traditional probability space are extended to the sub-linear expectation space.Based on the Pareto distribution,we obtain the weak law of large numbers and strong law of large numbers of the weighted sum of some independent random variable sequences.

编辑视角下语篇分析的线性表达

为便于编辑理清语篇内容推进路径,从语篇产生和理解角度入手,首先确定语篇分析基本单位为子目标,其次以一个周期内的句子比跨周期的句子具有更大的概念连贯性理论作为子目标之间的划界依据,最后根据自然顺序及堆栈原理利用子目标勾勒语篇的延展路径图,展示一种语篇多维信息的线性化描述方式。

A note on the cluster set of the law of the iterated logarithm under sub-linear expectations

In this note,we establish a compact law of the iterated logarithm under the upper capacity for independent and identically distributed random variables in a sub-linear expectation space.For showing the result,a self-normalized law of the iterated logarithm is established.

Calibration of CO and CO2 Monitors Used in Periodic Inspection of Vehicles at Fixed Stations for Environmental Control

Global efforts for environmental cleanliness through the control of gaseous emissions from vehicles are gaining momentum and attracting increasing attention. Calibration plays a crucial role in these efforts by ensuring the quantitative assessment of emissions for informed decisions on environmental treatments. This paper describes a method for the calibration of CO/CO2 monitors used for periodic inspections of vehicles in cites. The calibration was performed in the selected ranges: 900 - 12,000 µmol/mol for CO and 2000 - 20,000 µmol/mol for CO2. The traceability of the measurement results to the SI units was ensured by using certified reference materials from CO/N2 and CO2/N2 primary gas mixtures. The method performance was evaluated by assessing its linearity, accuracy, precision, bias, and uncertainty of the calibration results. The calibration data exhibited a strong linear trend with R² values close to 1, indicating an excellent fit between the measured values and the calibration lines. Precision, expressed as relative standard deviation (%RSD), ranged from 0.48 to 4.56% for CO and from 0.97 to 3.53% for CO2, staying well below the 5% threshold for reporting results at a 95% confidence level. Accuracy measured as percent recovery, was consistently high (≥ 99.1%) for CO and ranged from 84.90% to 101.54% across the calibration range for CO2. In addition, the method exhibited minimal bias for both CO and CO2 calibrations and thus provided a reliable and accurate approach for calibrating CO/CO2 monitors used in vehicle inspections. Thus, it ensures the effectiveness of exhaust emission control for better environment.

基于等效线性化的核电厂频域隔震分析方法研究

在核电构筑物土-结构相互作用(SSI)分析中常用的方法是子结构法,这是由于其采用半解析法地基模拟技术,具有求解速度快、分析系统频率稳定的优势。因此,可在隔震核电厂房楼层反应谱计算中采用子结构法。因隔震支座具有明显的非线性特征,而子结构法基于叠加原理,在求解非线性问题时具有局限性,为了能够采用子结构法求解隔震核电厂房地震响应问题,基于等效线性化理念,在子结构法中实现隔震支座非线性行为模拟,并用SAP 2000软件验证本方法的可行性。将该方法应用于不同地基参数下隔震厂房反应谱计算,将得到的反应谱与采用隔震支座等效刚度计算结果进行对比。研究结果表明,在子结构法中应用等效线性化方法得到的隔震支座滞回曲线与采用SAP2000软件得到的滞回曲线基本一致,证明该方法是可行的;与采用等效刚度计算结果相比,采用迭代收敛刚度计算出的零周期加速度变化较小,主频略降低,峰值略有提高;由于隔震系统卓越频率与场地卓越频率并不接近,因此隔震结构楼层反应谱对地基参数的变化并不敏感。