The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the...The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.展开更多
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
The m-widely orthant dependent(m-WOD)sequences are very weak dependent random variables.In the paper,the authors investigate the moving average processes,which is generated by m-WOD random variables.By using the tail ...The m-widely orthant dependent(m-WOD)sequences are very weak dependent random variables.In the paper,the authors investigate the moving average processes,which is generated by m-WOD random variables.By using the tail cut technique and maximum moment inequality of the m-WOD random variables,moment complete convergence and complete convergence of the maximal partial sums for the moving average processes are obtained,the results generalize and improve some corresponding results of the existing literature.展开更多
In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the ran...In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.展开更多
This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence ...This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.展开更多
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
In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some gen...In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.展开更多
In this paper, we investigate the complete convergence of double-indexed random- ly weighted sums of negatively orthant dependent （NOD） random variables. Some complete moment convergence and complete convergence of ...In this paper, we investigate the complete convergence of double-indexed random- ly weighted sums of negatively orthant dependent （NOD） random variables. Some complete moment convergence and complete convergence of this dependent sequence are presented, Marcinkiewicz-Zygmund-type strong law of large numbers is also obtained. Our results ex- tend some corresponding ones. In addition, some simulations are illustrated to show the convergence.展开更多
In this paper, we present a general method to prove the complete conver- gence for arrays of rowwise strong mixing random variables, and give some results on complete convergence under some suitable conditions. Some M...In this paper, we present a general method to prove the complete conver- gence for arrays of rowwise strong mixing random variables, and give some results on complete convergence under some suitable conditions. Some Marcinkiewicz-Zygmund type strong laws of large numbers are also obtained.展开更多
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
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
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
Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequal...Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequality for negative dependent sequence.Communications of the Korean Mathematical Society, 2007, 22(2): 315-321) and Nooghabi and Azarnoosh(Exponential inequality for negatively associated random variables. Statistical Papers, 2009, 50(2): 419-428). We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which improves the corresponding ones of Kim and Kim,and Nooghabi and Azarnoosh.展开更多
Under some conditions on probability, the author obtains some results on the complete convergence for partial sums of not necessary identically distributed p-mixing se- quences, and the complete convergence for partia...Under some conditions on probability, the author obtains some results on the complete convergence for partial sums of not necessary identically distributed p-mixing se- quences, and the complete convergence for partial sums of B-valued martingale differences is also studied. As application the author gives the corresponding results on the complete convergence for randomly indexed partial sums.展开更多
The convergence properties are studied through the analysis of （α,β）-mixing random variables sequences in different situations. By using the corresponding inequality, a convergence theorem was presented, and some ...The convergence properties are studied through the analysis of （α,β）-mixing random variables sequences in different situations. By using the corresponding inequality, a convergence theorem was presented, and some results for （α,β）-mixing random variables sequences with different distributions were obtained. The results extend the corresponding theorems of independent random variable sequences.展开更多
The author considers the contact process on a branching plane Td×Z, which is the product of a regular tree Td and the line Z. It is shown that above the second critical point, the complete convergence theory holds.
A maximal inequality for the partial sum of NA sequence is constructed. By using this inequality the complete convergence rates in the strong laws for a class of dependent random variables for weighted sums are discus...A maximal inequality for the partial sum of NA sequence is constructed. By using this inequality the complete convergence rates in the strong laws for a class of dependent random variables for weighted sums are discussed. The results obtained extend the results of Liang （1999, 2000）.展开更多
We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions.Consequently,we get the results for many dependent structures,such as END,ϱ^(*)mixing,ϱ^(-)mixing andφ-mixing,etc.
In this paper, the complete convergence of weighted sums for ρ＊-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete conver...In this paper, the complete convergence of weighted sums for ρ＊-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence of weighted sums for ρ＊-mixing sequence of random variables are established. We not only promote and improve the results of Li et al. （J. Theoret. Probab., 1995, 8（1）： 49--76） from i.i.d. to ρ＊-mixing setting but also obtain their necessities and relax their conditions.展开更多
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
基金supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)Re-accompanying Funding Project of Academic Achievements of Jingdezhen Ceramic University(Grant Nos.215/20506277,215/20506341)。
文摘The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.
基金National Natural Science Foundation of China (Grant Nos.12061028, 71871046)Support Program of the Guangxi China Science Foundation (Grant No.2018GXNSFAA281011)。
文摘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.
基金Supported by the Academic Funding Projects for Top Talents in Universities of Anhui Province (gxbjZD2022067, gxbjZD2021078)the Key Grant Project for Academic Leaders of Tongling University(2020tlxyxs31, 2020tlxyxs09)。
文摘The m-widely orthant dependent(m-WOD)sequences are very weak dependent random variables.In the paper,the authors investigate the moving average processes,which is generated by m-WOD random variables.By using the tail cut technique and maximum moment inequality of the m-WOD random variables,moment complete convergence and complete convergence of the maximal partial sums for the moving average processes are obtained,the results generalize and improve some corresponding results of the existing literature.
基金supported by a grant from Ferdowsi University of Mashhad(NO.2/42843)
文摘In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.
基金Supported by the National Natural Science Foundation of China（11061012） Supported by the Natural Science Foundation of Guangxi（2010GXNSFA013121）
文摘This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘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.
基金Supported by the National Natural Science Foundation of China(11501004,11501005,11526033,11671012)the Natural Science Foundation of Anhui Province(1508085J06,1608085QA02)+1 种基金the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)
文摘In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1150100511671012+8 种基金11701004)the Natural Science Foundation of Anhui Province(Grant Nos.1508085J061608085QA02)Science Research Project of Anhui Colleges(Grant Nos.KJ2015A065KJ2016A027KJ2017A027)Quality Engineering Project of Anhui Province(Grant Nos.2015jyxm054ZLTS2015053)Students Innovation Training Program of Anhui University(Grant No.201610357002)
文摘In this paper, we investigate the complete convergence of double-indexed random- ly weighted sums of negatively orthant dependent （NOD） random variables. Some complete moment convergence and complete convergence of this dependent sequence are presented, Marcinkiewicz-Zygmund-type strong law of large numbers is also obtained. Our results ex- tend some corresponding ones. In addition, some simulations are illustrated to show the convergence.
基金The NSF(11040606M04) of Anhui ProvinceNSF(11001052,10971097,10871001) of China
文摘In this paper, we present a general method to prove the complete conver- gence for arrays of rowwise strong mixing random variables, and give some results on complete convergence under some suitable conditions. Some Marcinkiewicz-Zygmund type strong laws of large numbers are also obtained.
文摘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.
基金Supported by the National Natural Science Foundation of China(11271161)
文摘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.
基金The NSF(11271020 and 11201004)of Chinathe NSF(10040606Q30 and 1208085MA11)of Anhui Provincethe NSF(KJ2012ZD01)of Education Department of Anhui Province
文摘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）.
基金Supported by the NSF of Anhui Province(1308085QA03,1408085QA02,1208085QA03)Supported by the Youth Science Research Fund of Anhui University+1 种基金Supported by the Students Innovative Training Project of Anhui University(201410357118)Supported by the Students Science Research Training Program of Anhui University(kyxl2013003)
文摘Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequality for negative dependent sequence.Communications of the Korean Mathematical Society, 2007, 22(2): 315-321) and Nooghabi and Azarnoosh(Exponential inequality for negatively associated random variables. Statistical Papers, 2009, 50(2): 419-428). We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which improves the corresponding ones of Kim and Kim,and Nooghabi and Azarnoosh.
文摘Under some conditions on probability, the author obtains some results on the complete convergence for partial sums of not necessary identically distributed p-mixing se- quences, and the complete convergence for partial sums of B-valued martingale differences is also studied. As application the author gives the corresponding results on the complete convergence for randomly indexed partial sums.
基金Supported by the Natural Science Foundation of Shandong Province(ZR2010FL016)
文摘The convergence properties are studied through the analysis of （α,β）-mixing random variables sequences in different situations. By using the corresponding inequality, a convergence theorem was presented, and some results for （α,β）-mixing random variables sequences with different distributions were obtained. The results extend the corresponding theorems of independent random variable sequences.
基金Research was supported in part by Grant G1999075106 from the Ministry of Science and Technology of China.
文摘The author considers the contact process on a branching plane Td×Z, which is the product of a regular tree Td and the line Z. It is shown that above the second critical point, the complete convergence theory holds.
基金Supported by Social Science Foundation of China(04BTJ003).
文摘A maximal inequality for the partial sum of NA sequence is constructed. By using this inequality the complete convergence rates in the strong laws for a class of dependent random variables for weighted sums are discussed. The results obtained extend the results of Liang （1999, 2000）.
基金Supported by the National Natural Science Foundation of China(11701403).
文摘We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions.Consequently,we get the results for many dependent structures,such as END,ϱ^(*)mixing,ϱ^(-)mixing andφ-mixing,etc.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1127102011201004)+2 种基金the Key Project of Chinese Ministry of Education(Grant No.211077)the Natural Science Foundation of Anhui Province(Grant Nos.10040606Q301208085MA11)
文摘In this paper, the complete convergence of weighted sums for ρ＊-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence of weighted sums for ρ＊-mixing sequence of random variables are established. We not only promote and improve the results of Li et al. （J. Theoret. Probab., 1995, 8（1）： 49--76） from i.i.d. to ρ＊-mixing setting but also obtain their necessities and relax their conditions.
基金The NSF(10901003) of Chinathe NSF(1208085MA11) of Anhui Provincethe NSF(KJ2012ZD01) of Education Department of Anhui Province
文摘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.
