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Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 98-113页

作者： LIU Zai-ming GENG Bing-zhen WANG Shi-jie School of Mathematics and statistics Central South UniversityChangsha 410083China School of big data and statistics Anhui UniversityHefei 230601China

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

关键词： bidimensional risk model asymptotic formula subexponential distribution consistently varying tail ruin probability

Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1127-1142页

作者： Yi WU Xue Jun WANG School of big data and Artificial Intelligence Chizhou UniversityChizhou 247000P.R.China School of big data and statistics Anhui UniversityHefei 230601P.R.China

Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1

关键词： Martingale difference random vectors weighted sums Marcinkiewicz–Zygmund type weak law of large numbers complete convergence strong law of large numbers multivariate simple linear regression model

Perpendicular-Cutdepth:Perpendicular Direction Depth Cutting data Augmentation Method

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Computers, Materials & Continua 2024年第4期79卷 927-941页

作者： Le Zou Linsong Hu Yifan Wang Zhize Wu Xiaofeng Wang Anhui Provincial Engineering Laboratory of big data Technology Application forUrban Infrastructure School ofArtificial Intelligence and Big DataHefei UniversityHefei230601China institute of Applied Optimization School of Artificial Intelligence and Big DataHefei UniversityHefei230601China

Depth estimation is an important task in computer vision.Collecting data at scale for monocular depth estimation is challenging,as this task requires simultaneously capturing RGB images and depth information.Therefore,data augmentation is crucial for this task.Existing data augmentationmethods often employ pixel-wise transformations,whichmay inadvertently disrupt edge features.In this paper,we propose a data augmentationmethod formonocular depth estimation,which we refer to as the Perpendicular-Cutdepth method.This method involves cutting realworld depth maps along perpendicular directions and pasting them onto input images,thereby diversifying the data without compromising edge features.To validate the effectiveness of the algorithm,we compared it with existing convolutional neural network(CNN)against the current mainstream data augmentation algorithms.Additionally,to verify the algorithm’s applicability to Transformer networks,we designed an encoder-decoder network structure based on Transformer to assess the generalization of our proposed algorithm.Experimental results demonstrate that,in the field of monocular depth estimation,our proposed method,Perpendicular-Cutdepth,outperforms traditional data augmentationmethods.On the indoor dataset NYU,our method increases accuracy from0.900 to 0.907 and reduces the error rate from0.357 to 0.351.On the outdoor dataset KITTI,our method improves accuracy from 0.9638 to 0.9642 and decreases the error rate from 0.060 to 0.0598.

关键词： Perpendicular depth estimation data augmentation

Asymptotic normality of error density estimator in stationary and explosive autoregressive models

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 140-158页

作者： WU Shi-peng YANG Wen-zhi GAO Min HU Shu-he School of Mathematical Sciences&School of big data and statistics Anhui UniversityHefei 230601China School of statistics Shanxi University of Finance and EconomicsTaiyuan030006China

In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.

关键词： explosive autoregressive models residual density estimator asymptotic distribution association sequence

On the convergence of tracking differentiator with multiple stochastic disturbances

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Science China(Information Sciences) 2024年第2期67卷 157-169页

作者： Zehao WU Huacheng ZHOU Baozhu GUO Feiqi DENG School of Mathematics and big data Foshan University School of Mathematics and statistics Central South University Academy of Mathematics and Systems Science Chinese Academy of Sciences Systems Engineering institute South China University of Technology

This paper investigates the convergence, noise-tolerance, and filtering performance of a tracking differentiator in the presence of multiple stochastic disturbances for the first time. We consider a general case wherein the input signal is corrupted by additive colored noise, and the tracking differentiator is disturbed by additive colored noise and white noise. The tracking differentiator is shown to track the input signal and its generalized derivatives in the mean square sense. Further, the almost sure convergence can be achieved when the stochastic noise affecting the input signal is vanishing. Herein, numerical simulations are performed to validate the theoretical results.

关键词： tracking differentiator convergence noise-tolerance filtering performance multiple stochastic disturbances

Effects of vacancy and external electric field on the electronic properties of the MoSi_(2)N_(4)/graphene heterostructure

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Chinese Physics B 2024年第3期33卷 542-550页

作者：梁前罗祥燕钱国林王远帆梁永超谢泉 College of big data and Information Engineering Institute of New Optoelectronic Materials and TechnologyGuizhou UniversityGuiyang 550025China

Recently,the newly synthesized septuple-atomic layer two-dimensional(2D)material MoSi_(2)N_(4)(MSN)has attracted attention worldwide.Our work delves into the effect of vacancies and external electric fields on the electronic properties of the MSN/graphene(Gr)heterostructure using first-principles calculation.We find that four types of defective structures,N-in,N-out,Si and Mo vacancy defects of monolayer MSN and MSN/Gr heterostructure are stable in air.Moreover,vacancy defects can effectively modulate the charge transfer at the interface of the MSN/Gr heterostructure as well as the work function of the pristine monolayer MSN and MSN/Gr heterostructure.Finally,the application of an external electric field enables the dynamic switching between n-type and p-type Schottky contacts.Our work may offer the possibility of exceeding the capabilities of conventional Schottky diodes based on MSN/Gr heterostructures.

关键词： MoSi_(2)N_(4) vacancy defects external electric field Schottky contacts

Graphene effectively activating "dead" water molecules between manganese dioxide layers in potassium-ion battery

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Journal of Energy Chemistry 2024年第6期93卷 306-315,I0008页

作者： Xinhai Wang Wensheng Yang Shengshang Lu Shangshu Peng Tong Guo Quan Xie Qingquan Xiao Yunjun Ruan institute of Advanced Optoelectronic Materials and Technology College of Big Data and Information EngineeringGuizhou UniversityGuiyang 550025GuizhouChina

Aqueous potassium-ion batteries(APIBs),recognized as safe and reliable new energy devices,are considered as one of the alternatives to traditional batteries.Layered MnO_(2),serving as the main cathode,exhibits a lower specific capacity in aqueous electrolytes compared to organic systems and operates through a different reaction mechanism.The application of highly conductive graphene may effectively enhance the capacity of APIBs but could complicate the potassium storage environment.In this study,a MnO_(2) cathode pre-intercalated with K~+ions and grown on graphene(KMO@rGO) was developed using the microwave hydrothermal method for APIBs.KMO@rGO achieved a specific capacity of 90 mA h g^(-1) at a current density of 0.1 A g^(-1),maintaining a capacity retention rate of>90% after 5000 cycles at 5 A g^(-1).In-situ and exsitu characterization techniques revealed the energy-storage mechanism of KMO@rGO:layered MnO_(2)traps a large amount of "dead" water molecules during K~+ions removal.However,the introduction of graphene enables these water molecules to escape during K~+ ions insertion at the cathode.The galvanostatic intermittent titration technique and density functional theory confirmed that KMO@rGO has a higher K~+ions migration rate than MnO_(2).Therefore,the capacity of this cathode depends on the interaction between dead water and K~+ions during the energy-storage reaction.The optimal structural alignment between layered MnO_(2) and graphene allows electrons to easily flow into the external circuit.Rapid charge compensation forces numerous low-solvent K~+ions to displace interlayer dead water,enhancing the capacity.This unique reaction mechanism is unprecedented in other aqueous battery studies.

关键词： Graphene K-ion batteries Mn-based layered oxide Water molecules Density functional theory

The Consistency of LSE Estimators in Partial Linear Regression Models under Mixing Random Errors

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1244-1272页

作者： Yun Bao YAO Yu Tan LÜ Chao LU Wei WANG Xue Jun WANG School of Mathematical Sciences Anhui UniversityHefei 230601P.R.China School of big data and Artificial Intelligence Chizhou UniversityChizhou 247000P.R.China School of big data and statistics Anhui UniversityHefei 230601P.R.China

In this paper,we consider the partial linear regression model y_(i)=x_(i)β^(*)+g(ti)+ε_(i),i=1,2,...,n,where(x_(i),ti)are known fixed design points,g(·)is an unknown function,andβ^(*)is an unknown parameter to be estimated,random errorsε_(i)are(α,β)-mix_(i)ng random variables.The p-th(p>1)mean consistency,strong consistency and complete consistency for least squares estimators ofβ^(*)and g(·)are investigated under some mild conditions.In addition,a numerical simulation is carried out to study the finite sample performance of the theoretical results.Finally,a real data analysis is provided to further verify the effect of the model.

关键词： (α,β)-mixing random variables partial linear regression model least squares estimator consistency

Measuring Financial Systemic Risk:Net Liability Clearing Mechanism and Contagion Effect

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Journal of Systems Science & Complexity 2024年第3期37卷 1114-1146页

作者： MA Jiali ZHU Shushang LI Duan College of big data statistics Guizhou University of Finance and EconomicsGuiyang 550025China School of Business Sun Yat-Sen UniversityGuangzhou 510275China School of data Science City University of Hong KongHong Kong 999077China

Following the framework of E-N model(Eisenberg and Noe,2001),the authors consider a new clearing mechanism based on net liabilities among financial institutions since the liabilities between the counterparties should be deducted accordingly when clearing in practice.As the basis for systemic risk measurement,similar to the original E-N model,the authors first establish some good properties for the clearing payment vector according to a more general model.Then,the authors investigate how risk spreads among institutions through the liability network forming the risk contagion channel.Finally,the authors illustrate with a specific example that the original E-N clearing mechanism may misidentify the systemic important institutions,and theoretically show that it may also overestimate the risk compared with the netting clearing mechanism.

关键词： Clearing mechanism contagion net liability network systemic risk