In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random vari...In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random variables,and another is for sub-orthogonal random variables.Both extend the strong law of large numbers for independent random variables under sublinear expectations to the non-independent case.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, 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.
This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and order...This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.展开更多
Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for ...Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,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.
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
By using the moment inequality, maximal inequality and the truncated method of random variables, we establish the strong law of large numbers of partial sums for pairwise NQD sequences, which extends the corresponding...By using the moment inequality, maximal inequality and the truncated method of random variables, we establish the strong law of large numbers of partial sums for pairwise NQD sequences, which extends the corresponding result of pairwise NQD random variables.展开更多
In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape ...In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.展开更多
For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array ...For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array in a real separable Banach space of typep,we establishL r convergence theorem and a general weak law of large numbers respectively,conversely,we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.展开更多
L_r convergence and convergence in probability for weighted sums of L_q-mixingale arrays have been discussed and the Marcinkiewicz type weak law of large numbers for L_q-mixingale arrays has been obtained.
In this paper, the Chung’s strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker tha...In this paper, the Chung’s strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker than that in Chung’s theorem. Some convergence theorems for martingale difference sequence such as Lp martingale difference sequence are the particular cases of results achieved in this paper. Finally, the convergence theorem for A-summability of sequence of random variables is proved, where A is a suitable real infinite matrix.展开更多
This paper introduces the concept of BC sequences and investigates some conditions which imply the strong law of large numbers for these sequences. The authors also study the strong law of large numbers for general ra...This paper introduces the concept of BC sequences and investigates some conditions which imply the strong law of large numbers for these sequences. The authors also study the strong law of large numbers for general random variable sequences. As applications of the result the authors characterize p-smoothableness of Banach space. Some generalizations of Petrov theorem, the Marcinkiewicz-Zygmund theorem and Hoffmann-J(?)rgensen and Pisier theorem are obtained.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
We investigate the strong law of large numbers(SLLN)for a large class of mean based on the Extended Negatively Dependent(END)sequences.The sufficient conditions are obtained for the mean of SLLN in this paper.As an im...We investigate the strong law of large numbers(SLLN)for a large class of mean based on the Extended Negatively Dependent(END)sequences.The sufficient conditions are obtained for the mean of SLLN in this paper.As an important application,the SLLN of Marcinkiewicz mean and logarithmic mean are presented immediately.In addition,we do some simulations for the mean of SLLN based on END 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, 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
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
文摘In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random variables,and another is for sub-orthogonal random variables.Both extend the strong law of large numbers for independent random variables under sublinear expectations to the non-independent case.
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Foundation item： Supported by the National Natural Science Foundation of China（11171001, 11201001） Supported by the Natural Science Foundation of Anhui Province（t208085QA03, 1308085QA03）
文摘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.
文摘This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.
基金Supported by National Basic Research Program of China(973 Program No.2007CBS14903)National Science Foundation of China(70671069)
文摘Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,
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 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.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117100112101001)+2 种基金Natural Science Foundation of Anhui Province(Grant No.1208085QA03)Talents Youth Fund of Anhui Province Universities(Grant No.2012SQRL204)Doctoral Research Start-up Funds Projects of Anhui University
文摘By using the moment inequality, maximal inequality and the truncated method of random variables, we establish the strong law of large numbers of partial sums for pairwise NQD sequences, which extends the corresponding result of pairwise NQD random variables.
基金Sponsored by the NSFC (10531070)Research Foundation for Outstanding Young Teachers of China University of Geoscience (Wuhan) (0816)
文摘In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.
基金Supported by the National Natural Science F oundation of China(No.10071058)
文摘For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array in a real separable Banach space of typep,we establishL r convergence theorem and a general weak law of large numbers respectively,conversely,we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.
文摘L_r convergence and convergence in probability for weighted sums of L_q-mixingale arrays have been discussed and the Marcinkiewicz type weak law of large numbers for L_q-mixingale arrays has been obtained.
基金Project supported by the National Natural Science Foundation of China (No. 10571159) and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 2002335090), China
文摘In this paper, the Chung’s strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker than that in Chung’s theorem. Some convergence theorems for martingale difference sequence such as Lp martingale difference sequence are the particular cases of results achieved in this paper. Finally, the convergence theorem for A-summability of sequence of random variables is proved, where A is a suitable real infinite matrix.
基金Supported by the National Natural Science Foundation of China(10071058)
文摘This paper introduces the concept of BC sequences and investigates some conditions which imply the strong law of large numbers for these sequences. The authors also study the strong law of large numbers for general random variable sequences. As applications of the result the authors characterize p-smoothableness of Banach space. Some generalizations of Petrov theorem, the Marcinkiewicz-Zygmund theorem and Hoffmann-J(?)rgensen and Pisier theorem are 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(Grant No.11701004)the Natural Science Foundation of Anhui Province(Grant Nos.1808085QA03,1808085QF212,1808085QA17)+2 种基金Provincial Natural Science Research Project of Anhui Colleges(Grant Nos.KJ2016A027,KJ2017A027,KJ2019A0006)Excellent Young Talents Research Project of Anhui Colleges(Grant No.gxyq2018102)Key Research Project of Suzhou University(Grant No.2017yzd16)。
文摘We investigate the strong law of large numbers(SLLN)for a large class of mean based on the Extended Negatively Dependent(END)sequences.The sufficient conditions are obtained for the mean of SLLN in this paper.As an important application,the SLLN of Marcinkiewicz mean and logarithmic mean are presented immediately.In addition,we do some simulations for the mean of SLLN based on END 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.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1127116161300204)
文摘In this paper, the Kolmogorov-Feller type weak law of large numbers are obtained, which extend and improve the related known works in the literature.
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 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].
