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职业本科《概率论与数理统计》课程的教学设计探索——以“中心极限定理(central limit theorem,CLT)”为例: 《装备制造与教育》2024年第4期64-69,共6页王惠刘林铖; 本文就职业本科的《概率论与数理统计》课程强调应用,中心极限定理为教学难点,传统教学方式效果不佳等问题对教学进行改进,引入具体问题,结合数学建模,使理论生动化。同时,利用Python进行数学实验,激发学生兴趣,促进主动学习。通过这种...; 关键词：职业本科概率论与数理统计中心极限定理教学设计

Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment: 《Acta Mathematica Sinica,English Series》2024年第8期1850-1874,共25页Chun Mao HUANG Rui ZHANG Zhi Qiang GAO; Supported by Shandong Provincial Natural Science Foundation(Grant No.ZR2021MA085);National Natural Science Foundation of China(Grant No.11971063)。; Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit t...; 关键词：Branching process with immigration random environment central limit theorem large deviation

Functional Shige Peng’s Central Limit Theorems for Martingale Vectors: 《Communications in Mathematics and Statistics》2024年第2期357-383,共27页Li-Xin Zhang; Supported by grants from the NSF of China(Grant No.11731012,12031005);Ten Thousands Talents Plan of Zhejiang Province(Grant No.2018R52042);NSF of Zhejiang Province(Grant No.LZ21A010002);the Fundamental Research Funds for the Central Universities.; In this paper,the functional central limit theorem is established for martingale like ran-dom vectors under the framework sub-linear expectations introduced by Shige Peng.As applications,the Lindeberg central limit th...; 关键词：Random vector Central limit theorem Functional central limit theorem Martingale difference Sub-linear expectation

Gaussian limit for determinantal point processes with J-Hermitian kernels: 《Science China Mathematics》2023年第6期1359-1374,共16页Zhaofeng Lin Yanqi Qiu Kai Wang; supported by National Natural Science Foundation of China (Grant Nos.Y7116335K1,11801547 and 11688101);supported by National Natural Science Foundation of China (Grant Nos.11722102 and 12026250);Shanghai Technology Innovation Project (Grant No.21JC1400800);Laboratory of Mathematics for Nonlinear Science,Ministry of Education of China。; We show that the central limit theorem for linear statistics over determinantal point processes with J-Hermitian kernels holds under fairly general conditions.In particular,we establish the Gaussian limit for linear s...; 关键词：determinantal point process J-Hermitian kernel linear statistics central limit theorem translation-invariantkernel

Fast-slow stochastic dynamical system with singular coefficients: 《Science China Mathematics》2023年第4期819-838,共20页Longjie Xie; supported by the Alexander von Humboldt foundation and National Natural Science Foundation of China(Grant Nos.12090011,12071186 and 11931004)。; This paper aims to study the asymptotic behavior of a fast-slow stochastic dynamical system with singular coefficients,where the fast motion is given by a continuous diffusion process while the slow component is drive...; 关键词：multi-scale dynamical system averaging principle central limit theorem α-stable process Zvonkin’s transformation

LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES: 《Acta Mathematica Scientia》2022年第5期2025-2039,共15页Naqi HUANG Yutao MA; supported by NSFC(12171038,11871008).; We use tridiagonal models to study the limiting behavior of β-Laguerre and β-Jacobi ensembles,focusing on the limiting behavior of the extremal eigenvalues and the central limit theorem for the two ensembles.For the...; 关键词：beta-ensembles largest and smallest eigenvalues central limit theorem total variationdistance

Recurrences for Callan's Generalization of Narayana Polynomials: 《Journal of Systems Science & Complexity》2022年第4期1573-1585,共13页CHEN Xi YANG Arthur Li Bo ZHAO James Jing Yu; supported by the National Natural Science Foundation of China under Grant No.11601062;the National Natural Science Foundation of China under Grant Nos.11971249;partially supported by the National Natural Science Foundation of China under Grant Nos.11771330 and 11971203;supported in part by the Fundamental Research Funds for the Central Universities under Grant Nos.11522110。; By using Chen,Hou and Mu’s extended Zeilberger algorithm,the authors obtain two recurrence relations for Callan’s generalization of Narayana polynomials.Based on these recurrence relations,the authors further prove ...; 关键词：Asymptotic normality Callan’s Narayana polynomials central limit theorem local limit theorem real zeros

CENTRAL LIMIT THEOREM AND CONVERGENCE RATES FOR A SUPERCRITICAL BRANCHING PROCESS WITH IMMIGRATION IN A RANDOM ENVIRONMENT被引量：2: 《Acta Mathematica Scientia》2022年第3期957-974,共18页Yingqiu LI Xulan HUANG Zhaohui PENG; supported by the National Natural Science Foundation of China(11571052,11731012);the Hunan Provincial Natural Science Foundation of China(2018JJ2417);the Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(2018MMAEZD02)。; We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in ...; 关键词：Branching process with immigration random environment convergence rates central limit theorem convergence in law convergence in probability

Is Evolution a Causal, Yet Not-Predetermined Process?: 《Journal of Modern Physics》2022年第5期707-721,共15页Maria K. Koleva; It is demonstrated that “survival of the fittest” approach suffers fundamental flaw planted in its very goal: reaching a uniform state starting from a minor random event. Simple considerations prove that a generic p...; 关键词：Stable Evolution Survival of the Fittest CAUSALITY Central Limit Theorem Decomposition Theorem Markov Process

Stable Central Limit Theorems for Super Ornstein–Uhlenbeck Processes,Ⅱ: 《Acta Mathematica Sinica,English Series》2022年第3期487-498,共12页Yan Xia REN Ren Ming SONG Zhen Yao SUN Jian Jie ZHAO; supported in part by NSFC(Grant Nos.11731009 and 12071011);the National Key R&D Program of China(Grant No.2020YFA0712900);supported in part by Simons Foundation(#429343,Renming Song)。; This paper is a continuation of our recent paper(Electron.J.Probab.,24(141),(2019))and is devoted to the asymptotic behavior of a class of supercritical super Ornstein-Uhlenbeck processes(X_(t))t≥0 with branching mec...; 关键词：SUPERPROCESSES Ornstein–Uhlenbeck processes stable distribution central limit theorem law of large numbers branching rate regime

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