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Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables
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作者 MENG Bing WU Qunying 《应用概率统计》 CSCD 北大核心 2024年第5期710-724,共15页
In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distri... In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them. 展开更多
关键词 ANA random variables complete convergence complete moment convergence weighted sums
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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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On the Strong Laws for Weighted Sums of m-negatively Asso ciated Random Variables 被引量:3
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作者 WU Yong-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第2期265-273,共9页
In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated(m-NA) random sample. The obtained results extend and improve the result of Qiu and Yang... In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated(m-NA) random sample. The obtained results extend and improve the result of Qiu and Yang in [1] to m-NA random variables. 展开更多
关键词 Marcinkiewicz-Zygmund strong law complete convergence weighted sums m-negatively associated random variable
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SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES 被引量:2
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作者 甘师信 陈平炎 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2388-2400,共13页
In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the c... In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3]. 展开更多
关键词 complete convergence weak convergence almost sure convergence ARRAY weighted sum NOD random variable sequence
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Almost Sure Convergence and Complete Convergence for the Weighted Sums of Martingale Differences 被引量:1
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《Wuhan University Journal of Natural Sciences》 CAS 1999年第3期278-284,共7页
Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are... Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption. 展开更多
关键词 complete convergence almost sure convergence weighted sums martingale differences moving average processes
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On complete convergence for Stout's type weighted sums of NOD sequence 被引量:1
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作者 YI Yan-chun HU Di CHEN Ping-yan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第3期340-346,共7页
In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup.The more optimal moment condition is give... In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup.The more optimal moment condition is given. The main results also hold for END sequence. 展开更多
关键词 NOD sequence Stout's type weighted sum complete convergence
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Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Extended Negatively Dependent Random Variables 被引量:1
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作者 LIU CUN-CHAO GUO MING-LE +1 位作者 ZHU DONG-JIN Wang De-hui 《Communications in Mathematical Research》 CSCD 2015年第1期40-50,共11页
By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively depe... By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. (Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8: 49-76) and Liang (Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48: 317-325). 展开更多
关键词 extended negatively dependent random variable complete convergence weighted sum
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ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES
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作者 甘师信 《Acta Mathematica Scientia》 SCIE CSCD 2010年第4期1021-1028,共8页
We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale differen... We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions. 展开更多
关键词 Strong law of large number almost sure convergence Lp convergence weighted sums Banach space valued random element sequence Banach space martingale difference sequence
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Almost Sure Convergence of Weighted Sums of NA Sequences
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作者 Cheng Riyan Gan Shixin 《Wuhan University Journal of Natural Sciences》 CAS 1998年第1期11-16,共6页
For double arrays of constants {a ni, 1≤i≤k n, n≥1} and NA r.v. 's {X n, n≥1}, conditions for almost sure convergence of are given. Both casesk n ↑ ∞ andk n=∞ are treated. A Marcinkiewicz-type theorem for ... For double arrays of constants {a ni, 1≤i≤k n, n≥1} and NA r.v. 's {X n, n≥1}, conditions for almost sure convergence of are given. Both casesk n ↑ ∞ andk n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case. 展开更多
关键词 a. s. convergence NA sequence weighted sum
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Complete Convergence of Weighted Sums for Arrays of Rowwise m-negatively Associated Random Variables
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作者 GUO MING-LE XU CHUN-YU ZHU DONG-JIN 《Communications in Mathematical Research》 CSCD 2014年第1期41-50,共10页
In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of co... In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables are established. These results generalize and complement some known conclusions. 展开更多
关键词 complete convergence negatively associated m-negatively associated weighted sum
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An Almost Sure Central Limit Theorem for Weighted Sums of Mixing Sequences
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作者 ZOU GUANG-YU ZHANG YONG 《Communications in Mathematical Research》 CSCD 2012年第4期359-366,共8页
In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather ar... In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables 展开更多
关键词 almost sure central limit theorem weighted sums mixing sequence logarithmic average
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Complete Convergence for Weighted Sums of WOD Random Variables
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作者 ZHANG Ying ZHANG Yu SHEN Ai-ting 《Chinese Quarterly Journal of Mathematics》 2016年第1期1-8,共8页
In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weight... In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent random variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables. 展开更多
关键词 widely orthant dependence complete convergence weighted sums
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Asymptotics for the joint tail probability of bidimensional randomly weighted sums with applications to insurance
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作者 Yang Yang Shaoying Chen Kam Chuen Yuen 《Science China Mathematics》 SCIE CSCD 2024年第1期163-186,共24页
This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectiv... This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually independent.Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence structures.As applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities. 展开更多
关键词 asymptotic joint tail behavior randomly weighted sum heavy-tailed distribution DEPENDENCE insurance risk model
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Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations
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作者 Feng-xiang FENG Ding-cheng WANG +1 位作者 Qun-ying WU Hai-wu HUANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2024年第3期862-874,共13页
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 fo... 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. 展开更多
关键词 sub-linear expectation complete convergence complete moment convergence the maximal weighted sums
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Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors
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作者 Yi WU Xue Jun WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第4期1127-1142,共16页
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... 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<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided. 展开更多
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
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Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables 被引量:3
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作者 Ji Gao YAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2018年第10期1501-1516,共16页
In this paper, the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated. Some sufficient conditions for the convergence are ... In this paper, the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated. Some sufficient conditions for the convergence are provided. In addition, the Marcinkiewicz Zygmund type strong law of large numbers for weighted sums of extended negatively dependent random variables is obtained. The results obtained in the article extend the corresponding ones for independent random variables and some dependent random variables. 展开更多
关键词 Extended negatively dependent complete convergence complete moment convergence maximal weighted sums strong law of large numbers
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Almost Sure Convergence of the General Jamison Weighted Sum of B-Valued Random Variables 被引量:3
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作者 ChunSu 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第1期181-192,共12页
In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed... In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables. 展开更多
关键词 Almost sure convergence β-valued random variable General Jamison weighted sum p-smooth Banach space Banach space of type p
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Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models 被引量:2
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作者 PENG Yunjie ZHENG Xiaoqian +2 位作者 YU Wei HE Kaixin WANG Xuejun 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2022年第1期342-360,共19页
This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random variables.Some sufficient conditions to prove the strong law of large numbers for wei... This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random variables.Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided.In particular,the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product.The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables.As an application,the authors investigate the errors-in-variables(EV,for short)regression models and establish the strong consistency for the least square estimators.Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration. 展开更多
关键词 EV regression models extended negatively dependent random variables strong consistency strong law of large numbers weighted sums
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Strong Convergence for Weighted Sums of Negatively Associated Arrays 被引量:2
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作者 Hanying LIANG Jingjing ZHANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2010年第2期273-288,共16页
Let {Xni} be an array of rowwise negatively associated random variables and Tnk=k∑i=1 i^a Xni for a ≥ -1, Snk =∑|i|≤k Ф(i/nη)1/nη Xni for η∈(0,1],where Ф is some function. The author studies necessary a... Let {Xni} be an array of rowwise negatively associated random variables and Tnk=k∑i=1 i^a Xni for a ≥ -1, Snk =∑|i|≤k Ф(i/nη)1/nη Xni for η∈(0,1],where Ф is some function. The author studies necessary and sufficient conditions of ∞∑n=1 AnP(max 1≤k≤n|Tnk|〉εBn)〈∞ and ∞∑n=1 CnP(max 0≤k≤mn|Snk|〉εDn)〈∞ for all ε 〉 0, where An, Bn, Cn and Dn are some positive constants, mn ∈ N with mn /nη →∞. The results of Lanzinger and Stadtmfiller in 2003 are extended from the i.i.d, case to the case of the negatively associated, not necessarily identically distributed random variables. Also, the result of Pruss in 2003 on independent variables reduces to a special case of the present paper; furthermore, the necessity part of his result is complemented. 展开更多
关键词 Tail probability Negatively associated random variable weighted sum
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Limiting Behavior of Weighted Sums of NOD Random Variables 被引量:3
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作者 De Hua QIU Ping Yan CHEN 《Journal of Mathematical Research and Exposition》 CSCD 2011年第6期1081-1091,共11页
The strong laws of large numbers and laws of the single logarithm for weighted sums of NOD random variables are established.The results presented generalize the corresponding results of Chen and Gan [5] in independent... The strong laws of large numbers and laws of the single logarithm for weighted sums of NOD random variables are established.The results presented generalize the corresponding results of Chen and Gan [5] in independent sequence case. 展开更多
关键词 NOD random variables strong laws of large numbers laws of single logarithm weighted sums.
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