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strong law of large numbers AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE

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Acta Mathematica Scientia 2001年第4期21卷 495-502页

作者：杨卫国刘文 Faculty of Science Jiangsu University of Science and Technology Zhenjiang 212013 China Hebei University of Technology Tianjin 300130 China

This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.

关键词： Cayley tree random field Markov chains field strong law of large numbers Shannon-McMillan theorem

strong law of large numbers and Complete Convergence for Sequences of -Mixing Random Variables

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Wuhan University Journal of Natural Sciences 2007年第2期12卷 211-217页

作者： GAN Shixin CHEN Pingyan QIU Dehua School of Mathematics and Statistics Wuhan University Wuhan 430072 Hubei China Department of Mathematics Jinan University Guangzhou 510630 Guangdong China Department of Mathematics and Computational Sciences Guangdong Business College Guangzhou 510320 GuangdongChina

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnum... 详细信息

关键词： strong law of large numbers complete convergence φ-mixing random variable sequence Wittmann's strong law oflarge numbers Teicher's strong law of large numbers

strong law of large numbers and Asymptotic Equipartition Probability for Nonsymmetric Markov Chain Indexed by Cayley Tree

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Journal of Mathematical Research and Exposition 2010年第6期30卷 976-984页

作者： Yan DONG Wei Guo YANG Department of Mathematics Shanghai Jiaotong UniversityShanghai 200240P.R.China Faculty of Science Jiangsu UniversityJiangsu 212013P.R.China

In this paper,we study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain（NSMC） indexed by Cayley tree with any finite *** asymptotic equipartition properties with almost everywhere（a.e.） convergence for NSMC indexed by Cayley tree are *** article generalizes a recent result.

关键词： strong law of large numbers nonsymmetric Markov chain Cayley tree asymptotic equipartition property.

A Remark on strong law of large numbers for Weighted U-Statistics

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Acta Mathematica Sinica,English Series 2014年第9期30卷 1595-1605页

作者： Hyung-Tae HA Mei Ling HUANG Department of Applied Statistics Gachon University Department of Mathematics and Statistics Brock University

Let （X, Xn; n≥ 1} be a sequence of i.i.d, random variables with values in a measurable space （S,8） such that E｜h（X1, X2,..., Xm）｜〈 ∞, where h is a measurable symmetric function from Sm into R = （-∞, ∞）. Let {wn,i1,i2 im ; 1 ≤ i1 〈 i2 〈 …… 〈im 〈 n, n ≥ m} be a matrix array of real numbers. Motivated by a result of Choi and Sung （1987）, in this note we are concerned with establishing a strong law of large numbers for weighted U-statistics with kernel h of degree m. We show that whenever SUP n≥m max1〈i1〈i2〈…〈im≤｜wn i1,i2 i,im｜〈∞, where 0 = Eh（X1, X2,..., Xm）. The proof of this result is based on a new general result on complete convergence, which is a fundamental tool, for array of real-valued random variables under some mild conditions.

关键词： strong law of large numbers weighted U-statistics complete convergence

On the strong law of large numbers for Non-Independent B-Valued Random Variables

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Wuhan University Journal of Natural Sciences 2004年第1期9卷 13-17页

作者： GanShi-xin SchoolofMathematicsandStatistics WuhanUniversityWuhan430072HubeiChina

This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgensen and Pisier theorem are obtained. Key words strong law of large numbers - Banach space valued random variable sequence - p-smoothable Banach space CLC number O 211.4 - O 211.6 Foundation item: Supported by the National Natural Science Foundation of China (10071058)Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.

关键词： strong law of large numbers Banach space valued random variable sequence p-smoothable Banach space

strong law of large numbers for Array of Rowwise AANA Random Variables

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Chinese Quarterly Journal of Mathematics 2014年第4期29卷 475-485页

作者： CHEN Zhi-yong LIU Ting-ting WANG Xue-jun LI Xiao-qin School of Mathematical Science Anhui University Hefei 230601 China

In this article, the strong laws of large numbers for array of rowwise asymptotically almost negatively associated(AANA) random variables are studied. Some sufficient conditions for strong laws of large numbers for array of rowwise AANA random variables are presented without assumption of identical distribution. Our results extend the corresponding ones for independent random variables to case of AANA random variables.

关键词： AANA random variables array of rowwise AANA random variables strong law of large numbers

On the strong law of large numbers for END Sequences

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Journal of Mathematical Research with Applications 2020年第4期40卷 432-440页

作者： Hao LI Xiaoqin LI Pengju DUAN School of Mathematics and Statistics Suzhou University School of Mathematical Sciences Anhui University

We investigate the strong law of large numbers(SLLN) for a large class of mean based on the Extended Negatively Dependent(END) sequences. The sufficient conditions are obtained for the mean of SLLN in this paper. As an important application, the SLLN of Marcinkiewicz mean and logarithmic mean are presented immediately. In addition, we do some simulations for the mean of SLLN based on END random variables.

关键词： strong law of large numbers Marcinkiewicz mean law logarithmic mean law END sequences

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 *** 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(1strong law of large numbers are established under some mild *** application to multivariate simple linear regression model is also provided.

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

Range-Renewal Processes:SLLNs and Power laws

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Chinese Annals of Mathematics,Series B 2022年第1期43卷 63-78页

作者： Xinxing CHEN Jiansheng XIE Jiangang YING School of Mathematical Sciences Shanghai Jiaotong UniversityShanghai 200240China School of Mathematical Sciences Fudan UniversityShanghai 200433China

Given n samples(viewed as an n-tuple)of aγ-regular discrete distributionπ,in this article the authors concern with the weighted and unweighted graphs induced by the n *** first prove a series of SLLN results(of Dvoretzky-Erdos'type).Then they show that the vertex weights of the graphs under investigation obey asymptotically power law distributions with exponent 1+γThey also give a conjecture that the degrees of unweighted graphs would exhibit asymptotically power law distributions with constant exponent *** exponent is obviously independent of the parameterγ∈(0,1),which is a surprise to us at first sight.

关键词： Range renewal process strong law of large numbers Power law