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Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables 被引量:3
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作者 GAN Shixin CHEN Pingyan QIU Dehua 《Wuhan University Journal of Natural Sciences》 CAS 2007年第2期211-217,共7页
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... 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 nnumbers for independent random variables are generalized to the case of φ -minxing random variables. 展开更多
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
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Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence 被引量:4
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作者 LIU Ting-ting CHEN Zhi-yong WANG Xue-jun WANG Xing-hui 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第4期578-584,共7页
In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.
关键词 strong law of large numbers weighted sums Ч-mixing sequence
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STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE 被引量:2
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作者 杨卫国 刘文 《Acta Mathematica Scientia》 SCIE CSCD 2001年第4期495-502,共8页
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 order... 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. 展开更多
关键词 Cayley tree random field Markov chains field strong law of large numbers Shannon-McMillan theorem
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STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES 被引量:2
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作者 包振华 叶中行 《Acta Mathematica Scientia》 SCIE CSCD 2007年第4期829-837,共9页
Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields (NSMC) on Cayley trees are studied. In the proof, a new technique for ... Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields (NSMC) on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere (a,e.) convergence for NSMC on Cayley trees are obtained, 展开更多
关键词 Cayley tree nonsymmetric Markov chain fields strong law of large numbers asymptotic equipartition property
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On Strong Law of Large Numbers for Random Sequence 被引量:1
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作者 WANG Zhong-zhi 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第4期475-480,共6页
This note is devoted to introduce a new concept of conditionally dominated random variables.Under suitable restrict conditions,a general strong law of large numbers for arbitrary continuous random variables is obtained.
关键词 random variable strong law of large numbers conditionally dominated random sequence
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Strong Law of Large Numbers for Array of Rowwise AANA Random Variables 被引量:1
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作者 CHEN Zhi-yong LIU Ting-ting WANG Xue-jun LI Xiao-qin 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第4期475-485,共11页
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 ar... 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. 展开更多
关键词 AANA random variables array of rowwise AANA random variables strong law of large numbers
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LYAPOUNOLYAPOUNOV EXPONENTS AND LAW OF LARGE NUMBERS FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES
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作者 毛明志 韩东 《Acta Mathematica Scientia》 SCIE CSCD 2009年第5期1383-1394,共12页
In this article, the authors mainly discuss the law of large number under Kalikow's condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape ... In this article, the authors mainly discuss the law of large number under Kalikow's condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation. 展开更多
关键词 random walk random environment Lyapounov exponents law of large numbers renewal structure
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A note on strong law of large numbers of random variables
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作者 LIN Zheng-yan SHEN Xin-mei 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第6期1088-1091,共4页
In this paper, the Chung’s strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker tha... In this paper, the Chung’s strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker than that in Chung’s theorem. Some convergence theorems for martingale difference sequence such as Lp martingale difference sequence are the particular cases of results achieved in this paper. Finally, the convergence theorem for A-summability of sequence of random variables is proved, where A is a suitable real infinite matrix. 展开更多
关键词 Strong law of large numbers (SLLN) Martingale difference sequence A-summable sequence
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ON THE STRONG LAW OF LARGE NUMBERS
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作者 邱德华 甘师信 《Acta Mathematica Scientia》 SCIE CSCD 2005年第3期525-532,共8页
This paper introduces the concept of BC sequences and investigates some conditions which imply the strong law of large numbers for these sequences. The authors also study the strong law of large numbers for general ra... This paper introduces the concept of BC sequences and investigates some conditions which imply the strong law of large numbers for these sequences. The authors also study the strong law of large numbers for general random variable sequences. As applications of the result the authors characterize p-smoothableness of Banach space. Some generalizations of Petrov theorem, the Marcinkiewicz-Zygmund theorem and Hoffmann-J(?)rgensen and Pisier theorem are obtained. 展开更多
关键词 BC random variable sequence p-smoothable Banach space the strong law of large numbers
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On the Strong Law of Large Numbers for Non-Independent B-Valued Random Variables
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作者 GanShi-xin 《Wuhan University Journal of Natural Sciences》 EI CAS 2004年第1期13-17,共5页
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?rgen... 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. 展开更多
关键词 strong law of large numbers Banach space valued random variable sequence p-smoothable Banach space
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Characterization of Type p Banach Spaces by the Weak Law of Large Numbers
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作者 Gan Shi-xin 《Wuhan University Journal of Natural Sciences》 EI CAS 2002年第1期14-19,共6页
For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array ... For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array in a real separable Banach space of typep,we establishL r convergence theorem and a general weak law of large numbers respectively,conversely,we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums. 展开更多
关键词 Banach space of typep array of random elements weighted sums weak law of large numbers {a nj} uniform integrability L r convergence convergence in probability
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Strong Laws of Large Numbers for Fuzzy Set-Valued Random Variables in Gα Space
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作者 Lamei Shen Li Guan 《Advances in Pure Mathematics》 2016年第9期583-592,共10页
In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>&infin;</sup><sub>H</sub> . The results are based on the result ... In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>&infin;</sup><sub>H</sub> . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2]. 展开更多
关键词 laws of large numbers Fuzzy Set-Valued Random Variable Hausdorff Metric
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STRONG LAW OF LARGE NUMBERS AND GROWTH RATE FOR NOD SEQUENCES
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作者 MA Song-lin WANG Xue-jun 《巢湖学院学报》 2015年第3期1-6,39,共7页
In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)a... In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)and the strong law of large numbers and strong growth rate for negatively orthant dependent sequences. 展开更多
关键词 negatively orthant dependent sequences strong law of large numbers growth rate
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Stochastic Model of Dengue: Analysing the Probability of Extinction and LLN
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作者 Ragnimwendé Sawadogo Fourtoua Victorien Konané Wahabo Baguian 《Applied Mathematics》 2024年第9期594-613,共20页
In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using th... In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable. 展开更多
关键词 Dengue Fever Continuous-Time Markov Chain Multitype Branching Process Probability of Disease Extinction law of large numbers
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The Sufficient and Necessary Conditions of the Strong Law of Large Numbers under Sub-linear Expectations
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作者 Li Xin ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第12期2283-2315,共33页
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 ... 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. 展开更多
关键词 Sub-linear expectation capacity strong convergence law of large numbers
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A strong law of large numbers under sublinear expectations
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作者 Yongsheng Song 《Probability, Uncertainty and Quantitative Risk》 2023年第3期333-350,共18页
We consider a sequence of independent and identically distributed(i.i.d.)random variables{ξ_(k)}under a sublinear expectation E=sup_(P∈Θ).We first give a new proof to the fact that,under each P∈Θ,any cluster poin... We consider a sequence of independent and identically distributed(i.i.d.)random variables{ξ_(k)}under a sublinear expectation E=sup_(P∈Θ).We first give a new proof to the fact that,under each P∈Θ,any cluster point of the empirical averages.Next,we consider sublinear expectations on a Polish space,and show that for each constantμ∈[μ,μ^(-)],there exists a probability P_(μ)∈Θsuch thatlim_(n→∞)ξ_(n)=μ,P_(μ-a.s.,(0.1))supposing thatΘis weakly compact and.Under the same conditions,we obtain a generalization of(0.1)in the product space with replaced by.Here is a Borel measurable function on,.Finally,we characterize the triviality of the tail-algebra of the i.i.d.random variables under a sublinear expectation. 展开更多
关键词 law of large numbers Tailσ-algebra Sublinear expectation
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CONVERGENCE RATES IN THE STRONG LAWS OF NONSTATIONARYρ~*-MIXING RANDOM FIELDS 被引量:8
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作者 张立新 《Acta Mathematica Scientia》 SCIE CSCD 2000年第3期303-312,共10页
By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing... By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields. 展开更多
关键词 Rosenthal type inequality strong law of large numbers *-mixing random fields
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LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES 被引量:8
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作者 胡亦钧 明瑞星 杨文权 《Acta Mathematica Scientia》 SCIE CSCD 2007年第4期886-896,共11页
M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large devi... M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given. 展开更多
关键词 negatively associated random variables stationary sequence strong law of large numbers large deviations moderate deviations
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Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree 被引量:23
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作者 HUANG HuiLin~1 YANG WeiGuo~(2+) 1 Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China 2 Faculty of Science,Jiangsu University,Zhenjiang 212013,China 《Science China Mathematics》 SCIE 2008年第2期195-202,共8页
In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a h... In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree. 展开更多
关键词 Markov chains Shannon-McMillan theorem strong law of large numbers uniformly bounded tree 60F15 60J10
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Multi-dimensional Central Limit Theorems and Laws of Large Numbers under Sublinear Expectations 被引量:4
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作者 Ze Chun HU Ling ZHOU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第2期305-318,共14页
In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.
关键词 Central limit theorem law of large numbers sublinear expectation
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