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
We study a new family of random variables that each arise as the distribution of the maximum or minimum of a random number N of i.i.d. random variables X<sub>1</sub>, X<sub>2</sub>,…, X<sub...We study a new family of random variables that each arise as the distribution of the maximum or minimum of a random number N of i.i.d. random variables X<sub>1</sub>, X<sub>2</sub>,…, X<sub>N</sub>, each distributed as a variable X with support on [0, 1]. The general scheme is first outlined, and several special cases are studied in detail. Wherever appropriate, we find estimates of the parameter θ in the one-parameter family in question.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 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
In this paper we present some results for the general strong laws of large numbers of p-mixing random variables by a maximal inequality of Utev and Peligrad. These results extend and improve the related known works in...In this paper we present some results for the general strong laws of large numbers of p-mixing random variables by a maximal inequality of Utev and Peligrad. These results extend and improve the related known works in the literature.展开更多
In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable ob...In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable obtained by Taylor [1].展开更多
In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient condit...In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient conditions of strong law of large numbers for the difference of random variables which independent and identically distributed conditions are regarded. In this study, we consider the limit as which is stronger than the limit as m× n→?∞ when m, n →?∞?are natural numbers.展开更多
In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the ...In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.展开更多
In this paper, the authors study the strong law of large numbers for partial sums of pairwise negatively quadrant dependent （NQD） random variables. The results obtained improve the corresponding theorems of Hu et a...In this paper, the authors study the strong law of large numbers for partial sums of pairwise negatively quadrant dependent （NQD） random variables. The results obtained improve the corresponding theorems of Hu et al. （2013）, and Qiu and Yang （2006） under some weaker conditions.展开更多
This paper investigates some conditions which imply the strong laws of large numbers for Bana ch space val-ued random variable sequences.Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jdprg...This paper investigates some conditions which imply the strong laws of large numbers for Bana ch space val-ued random variable sequences.Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jdprgensen and Pisier theorem are obtained.展开更多
In this paper, Wittmann type strong laws of large numbers for blockwise mnegatively associated random variables are established which extend and improve the related known works in the literature.
In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</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>∞</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
In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑...In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/｜n｜（log｜n｜dP（｜Sn/Vn｜≥ε√log log｜n｜） and ∑n（logn｜）b/｜n｜（log｜n｜）^d-1P（｜Sn/Vn｜≥ε√log n）,as ε↓0,is established.展开更多
We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to c...We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.展开更多
In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {xn,n≥1} and two sequences of positive...In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {xn,n≥1} and two sequences of positive numbers {an,n≥1} and {bn,n≥1} there exist d dn∈R,n = 1,2,..., such that bn^-1∑i=1^naixi-dn→0 a.s.under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables.展开更多
In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial...In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.展开更多
In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent ...In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.展开更多
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.
Convergence properties for arrays of rowwise φ-mixing random variables are studied. As an application, the Chung-type strong law of large numbers for arrays of rowwise φ-mixing random variables is obtained. Our resu...Convergence properties for arrays of rowwise φ-mixing random variables are studied. As an application, the Chung-type strong law of large numbers for arrays of rowwise φ-mixing random variables is obtained. Our results extend the corresponding ones for independent random variables to the case of φ-mixing random variables.展开更多
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
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.
文摘We study a new family of random variables that each arise as the distribution of the maximum or minimum of a random number N of i.i.d. random variables X<sub>1</sub>, X<sub>2</sub>,…, X<sub>N</sub>, each distributed as a variable X with support on [0, 1]. The general scheme is first outlined, and several special cases are studied in detail. Wherever appropriate, we find estimates of the parameter θ in the one-parameter family in question.
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（lilT1001, 11201001） Supported by the Natural Science Foundation of Anhui Province（1208085QA03）+1 种基金 Supported by the Talents Youth Fund of Anhui Province Universities（2012SQRL204） Supported by th Doctoral Research Start-up Funds Projects of Anhui University（33190250）
文摘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.
文摘In this paper we present some results for the general strong laws of large numbers of p-mixing random variables by a maximal inequality of Utev and Peligrad. These results extend and improve the related known works in the literature.
文摘In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable obtained by Taylor [1].
文摘In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient conditions of strong law of large numbers for the difference of random variables which independent and identically distributed conditions are regarded. In this study, we consider the limit as which is stronger than the limit as m× n→?∞ when m, n →?∞?are natural numbers.
文摘In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.
基金Supported by the Humanities and Social Sciences Foundation for the Youth Scholars of Ministry of Education ofChina(Grant No.12YJCZH217)the Natural Science Foundation of Anhui Province(Grant No.1308085MA03)College Excellent Young Talents Fund Project of the Anhui Province(Grant No.2011SQRL143)
文摘In this paper, the authors study the strong law of large numbers for partial sums of pairwise negatively quadrant dependent （NQD） random variables. The results obtained improve the corresponding theorems of Hu et al. （2013）, and Qiu and Yang （2006） under some weaker conditions.
基金Supported by the National Natrual Science Foun dation of ChiYla(10071058)
文摘This paper investigates some conditions which imply the strong laws of large numbers for Bana ch space val-ued random variable sequences.Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jdprgensen and Pisier theorem are obtained.
基金Supported by the National Natural Science Foundation of China(Grant No.11271161)
文摘In this paper, Wittmann type strong laws of large numbers for blockwise mnegatively associated random variables are established which extend and improve the related known works in the literature.
文摘In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</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].
文摘In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/｜n｜（log｜n｜dP（｜Sn/Vn｜≥ε√log log｜n｜） and ∑n（logn｜）b/｜n｜（log｜n｜）^d-1P（｜Sn/Vn｜≥ε√log n）,as ε↓0,is established.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.
基金Supported by the National Natural Science Foundation of China(10671149)
文摘In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {xn,n≥1} and two sequences of positive numbers {an,n≥1} and {bn,n≥1} there exist d dn∈R,n = 1,2,..., such that bn^-1∑i=1^naixi-dn→0 a.s.under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables.
基金Supported by the Natural Science Foundation of Anhui Province（1508085J06） the Key Projects for Academic Talent of Anhui Province（gxbj ZD2016005） the Students Innovative Training Project of Anhui University（201610357001）
文摘In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.
基金Supported by the University Students Science Research Training Program of Anhui University(KYXL20110004)
文摘In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.
基金Supported by the National Nature Science Foundation of China（10571076） Supported by Anhui High Education Research（2006Kj246B）
文摘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.
基金the National Natural Science Foundation of China(Grant Nos.1117100111301004+5 种基金11326172)the Natural Science Foundation of Anhui Province(Grant No.1408085QA02)Talents Youth Fund of Anhui ProvinceUniversities(Grant No.2012SQRL204)the Students Science Research Training Program of Anhui University(Grant Nos.KYXL2014013KYXL2014016)Doctoral Research Start-up Funds Projects of Anhui University
文摘Convergence properties for arrays of rowwise φ-mixing random variables are studied. As an application, the Chung-type strong law of large numbers for arrays of rowwise φ-mixing random variables is obtained. Our results extend the corresponding ones for independent random variables to the case of φ-mixing random variables.
基金Partly supported by the National Natural Science Foundation of China and the Ministry of Education of ChinaPartly supported by the Science and Technology Research Item of Hubei Provincial Department of Education,Jiaghan University
文摘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.
