In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of r...In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of results on complete moment convergence for ND random variables under the sub-linear expectations.展开更多
In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing th...In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.展开更多
It is well-known that the complete convergence theorem for i.i.d, random vari- ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4] obtained a moment version of Hsu and Robbins se...It is well-known that the complete convergence theorem for i.i.d, random vari- ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4] obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever c goes to zero, so it is of interest to investigate the asymptotic behavior of the series as e goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.展开更多
Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an ap...Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an application, Marcinkiewicz-Zygmundtype strong law of large numbers for this moving average process is presented in this paper.展开更多
In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the correspondin...In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature.展开更多
For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergenc...For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE(max1≤k≤n|Sk|^1/q-∈bn^1/qp)^+〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 (log n) ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.展开更多
In the paper we extend and generalize some results of complete moment convergence results (or the refinement of complete convergence) obtained by Chow [On the rate of moment complete convergence of sample sums and e...In the paper we extend and generalize some results of complete moment convergence results (or the refinement of complete convergence) obtained by Chow [On the rate of moment complete convergence of sample sums and extremes. Bull. Inst. Math. Academia Sinica, 16, 177-201 (1988)] and Li & Spataru [Refinement of convergence rates for tail probabilities. J. Theor. Probab., 18, 933-947 (2005)] to sequences of identically distributed φ-mixing random variables.展开更多
In this paper,the complete convergence and the complete moment convergence for extended negatively dependent(END,in short) random variables without identical distribution are investigated.Under some suitable condition...In this paper,the complete convergence and the complete moment convergence for extended negatively dependent(END,in short) random variables without identical distribution are investigated.Under some suitable conditions,the equivalence between the moment of random variables and the complete convergence is established.In addition,the equivalence between the moment of random variables and the complete moment convergence is also proved.As applications,the Marcinkiewicz-Zygmund-type strong law of large numbers and the Baum-Katz-type result for END random variables are established.The results obtained in this paper extend the corresponding ones for independent random variables and some dependent random variables.展开更多
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
In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type The...In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for martingale diference sequence.As an application,a strong law of large numbers for martingale diference sequence is obtained.展开更多
In this paper, we study the complete q-moment convergence of moving average processes under v-mixing assumption. The results obtained not only extend some previous known results, but also improve them.
In this paper, complete moment convergence for widely orthant dependent random vari- ables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results ...In this paper, complete moment convergence for widely orthant dependent random vari- ables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.展开更多
We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math...We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math.Inequal.,2019,13(1):251–260].As an application of the main results,we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.展开更多
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
The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding c...The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates (or complete moment convergence) for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.展开更多
基金the National Natural Science Foundation of China(71871046,11661029)Natural Science Foundation of Guangxi(2018JJB110010)。
文摘In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of results on complete moment convergence for ND random variables under the sub-linear expectations.
基金supported by the National Science Foundation of China(11271161)
文摘In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.
基金supported by National Natural Science Foundation of China(11171303,61273093)the Specialized Research Fund for the Doctor Program of Higher Education(20090101110020)
文摘It is well-known that the complete convergence theorem for i.i.d, random vari- ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4] obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever c goes to zero, so it is of interest to investigate the asymptotic behavior of the series as e goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.
基金Supported by the National Natural Science Foundation of China(11501005, 11526033) Supported by the Natural Science Foundation of Anhui Province(1408085QA02, 1508085J06, 1608085QA02)+3 种基金 Supported by the Provincial Natural Science Research Project of Anhui Colleges(KJ2014A020, KJ2015A065) Supported by the Quality Engineering Project of Anhui Province(2015jyxm054) Supported by the Students Science Research Training Program of Anhui University(KYXL2014016, KYXL2014013) Supported by the Applied Teaching Model Curriculum of Anhui University(XJYYKC1401, ZLTS2015053)
文摘Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an application, Marcinkiewicz-Zygmundtype strong law of large numbers for this moving average process is presented in this paper.
基金Supported by National Natural Science Foundation of China(Grant No.11271161)
文摘In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature.
基金supported by National Natural Science Foundation of China (Grant No. 10871146)supported by Natural Sciences and Engineering Research Council of Canada
文摘For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE(max1≤k≤n|Sk|^1/q-∈bn^1/qp)^+〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 (log n) ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.
基金supported by National Natural Science Foundation of China (Grant No. 60574002)supported by MASCOS grant from Australian Research CouncilNational Natural Science Foundation of China (Grant No. 70671018)
文摘In the paper we extend and generalize some results of complete moment convergence results (or the refinement of complete convergence) obtained by Chow [On the rate of moment complete convergence of sample sums and extremes. Bull. Inst. Math. Academia Sinica, 16, 177-201 (1988)] and Li & Spataru [Refinement of convergence rates for tail probabilities. J. Theor. Probab., 18, 933-947 (2005)] to sequences of identically distributed φ-mixing random variables.
基金supported by the National Natural Science Foundation of China(Nos.11501004,11501005,11526033)the Natural Science Foundation of Anhui Province(No.1508085J06)+4 种基金the Key Projects for Academic Talent of Anhui Province(No.gxbj ZD2016005)the Provincial Natural Science Research Project of Anhui Colleges(No.KJ2015A018)the Open Project of School of Mathematical Sciences,Anhui University(No.ADSY201503)the Quality Engineering Project of Anhui Province(No.2015jyxm045)the Quality Improvement Projects for Undergraduate Education of Anhui University(No.ZLTS2015035)
文摘In this paper,the complete convergence and the complete moment convergence for extended negatively dependent(END,in short) random variables without identical distribution are investigated.Under some suitable conditions,the equivalence between the moment of random variables and the complete convergence is established.In addition,the equivalence between the moment of random variables and the complete moment convergence is also proved.As applications,the Marcinkiewicz-Zygmund-type strong law of large numbers and the Baum-Katz-type result for END random variables are established.The results obtained in this paper extend the corresponding ones for independent random variables and some dependent random variables.
基金Supported by National Natural Science Foundation of China(Grant Nos.11401415 and 11571250)
文摘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.
基金Supported by National Natural Science Foundation of China(Grant Nos.11201001,11171001,11126176 and 11226207)Natural Science Foundation of Anhui Province(Grant Nos.1208085QA03 and 1308085QA03)+2 种基金Applied Teaching Model Curriculum of Anhui University(Grant No.XJYYXKC04)Students Innovative Training Project of Anhui University(Grant No.201310357004)Doctoral Research Start-up Funds Projects of Anhui University and the Students Science Research Training Program of Anhui University(Grant No.KYXL2012007)
文摘In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for martingale diference sequence.As an application,a strong law of large numbers for martingale diference sequence is obtained.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1087100110971097)+1 种基金the Anhui Provincial Natural Science Foundation of China (Grant No.11040606M04)the Anhui Province College Excellent Young Talents Fundation of China (Grant No.2009SQRZ176ZD)
文摘In this paper, we study the complete q-moment convergence of moving average processes under v-mixing assumption. The results obtained not only extend some previous known results, but also improve them.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671012,11501004 and 11501005)the Natural Science Foundation of Anhui Province(Grant No.1508085J06)+1 种基金the Key Projects for Academic Talent of Anhui Province(Grant No.gxbjZD2016005)the Research Teaching Model Curriculum of Anhui University(Grant No.xjyjkc1407)
文摘In this paper, complete moment convergence for widely orthant dependent random vari- ables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.
基金China(Grant Nos.11671012,11871072)the Natural Science Foundation of Anhui Province(1808085QA03,1908085QA01,1908085QA07)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0001,KJ2019A0003)the Students Innovative Training Project of Anhui University(S201910357342).
文摘We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math.Inequal.,2019,13(1):251–260].As an application of the main results,we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.
基金supported by the Natural Science Foundation of Guangxi(Grant No.2024GXNSFAA010476)the National Natural Science Foundation of China(Grant No.12361031)。
文摘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.
基金National Natural Science Foundation of China (Grant No.60574002)MASCOS grant from Australian Research CouncilNational Natural Science Foundation of China (Grant No.70671018)
文摘The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates (or complete moment convergence) for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.