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
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
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
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, 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
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
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 article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong...In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.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,we establish a Rosenthal-type inequality of partial sums for ρ~mixing random variables.As its applications,we get the complete convergence rates in the strong laws for ρ^-mixing random variables.The re...In this paper,we establish a Rosenthal-type inequality of partial sums for ρ~mixing random variables.As its applications,we get the complete convergence rates in the strong laws for ρ^-mixing random variables.The result obtained extends the corresponding result.展开更多
In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences a...In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.展开更多
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
In the paper, the complete convergence for arrays of rowwise Q-mixing random variables is studied. Some sufficient conditions for complete convergence for an array of row wise Q-mixing random variables without assumpt...In the paper, the complete convergence for arrays of rowwise Q-mixing random variables is studied. Some sufficient conditions for complete convergence for an array of row wise Q-mixing random variables without assumptions of identical distribution and stochastic domination are presented.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
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
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.
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
Rosenthal inequality for NOD （negatively＇ orthant dependent） random variable sequences is established. As its applications, two theorems of complete convergence of weighted sums for arrays of NOD random variables a...Rosenthal inequality for NOD （negatively＇ orthant dependent） random variable sequences is established. As its applications, two theorems of complete convergence of weighted sums for arrays of NOD random variables are given, which extend the corresponding known results.展开更多
Based on fuzzy random variables, the concept of fuzzy stochastic sequences is defined. Strong limit theorems for fuzzy stochastic sequences are established. Some known results in non-fuzzy stochastic sequences are ext...Based on fuzzy random variables, the concept of fuzzy stochastic sequences is defined. Strong limit theorems for fuzzy stochastic sequences are established. Some known results in non-fuzzy stochastic sequences are extended. In order to prove results of this paper, the notion of fuzzy martingale difference sequences is also introduced.展开更多
Consider a ρ-mixing sequence of identically distributed random variables with the underlying dis- tribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm...Consider a ρ-mixing sequence of identically distributed random variables with the underlying dis- tribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm holds for ρ-mixing sequences of random variables. Our results generalize and improve Theorems 1.2-1.3 of Qi and Cheng （1996） from the i.i.d, case to ρ-mixing sequences.展开更多
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（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 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 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.
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 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the National Natural Science Foundation of China(10671149)
文摘In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.
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 Science Foundation（10661006） Supported by Innovation Project of Guangxi Graduate Education（2007105960812M18）
文摘In this paper,we establish a Rosenthal-type inequality of partial sums for ρ~mixing random variables.As its applications,we get the complete convergence rates in the strong laws for ρ^-mixing random variables.The result obtained extends the corresponding result.
基金The NSF(10871001,60803059) of ChinaTalents Youth Fund(2010SQRL016ZD) of Anhi Province Universities+2 种基金Youth Science Research Fund(2009QN011A) of Anhui UniversityProvincial Natural Science Research Project of Anhui Colleges(KJ2010A005)Academic innovation team of Anhui University (KJTD001B)
文摘In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.
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Supported by the Talents Youth Fund of Anhui Province Universities(2012SQRL204)
文摘In the paper, the complete convergence for arrays of rowwise Q-mixing random variables is studied. Some sufficient conditions for complete convergence for an array of row wise Q-mixing random variables without assumptions of identical distribution and stochastic domination are presented.
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.
文摘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].
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 (10671149,60574002)
文摘Rosenthal inequality for NOD （negatively＇ orthant dependent） random variable sequences is established. As its applications, two theorems of complete convergence of weighted sums for arrays of NOD random variables are given, which extend the corresponding known results.
基金Supported by National Basic Research Programof China (973Program, No.2007CB814901)Research Funds for Doctorial Programs of Higher Education (No.20060255006)Anhui Natural Science Foundation of University (No. KJ2008B143)
文摘Based on fuzzy random variables, the concept of fuzzy stochastic sequences is defined. Strong limit theorems for fuzzy stochastic sequences are established. Some known results in non-fuzzy stochastic sequences are extended. In order to prove results of this paper, the notion of fuzzy martingale difference sequences is also introduced.
基金supported by the National Natural Science Foundation of China(11361019)the Support Program of the Guangxi China Science Foundation(2015GXNSFAA139008)
文摘Consider a ρ-mixing sequence of identically distributed random variables with the underlying dis- tribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm holds for ρ-mixing sequences of random variables. Our results generalize and improve Theorems 1.2-1.3 of Qi and Cheng （1996） from the i.i.d, case to ρ-mixing sequences.
