STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE

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.

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

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.

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

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,

Strong Law of Large Numbers for Array of Rowwise AANA Random Variables

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.

ON THE STRONG LAW OF LARGE NUMBERS

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.

On the Strong Law of Large Numbers for Non-Independent B-Valued Random Variables

This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgensen and Pisier theorem are obtained. Key words strong law of large numbers - Banach space valued random variable sequence - p-smoothable Banach space CLC number O 211.4 - O 211.6 Foundation item: Supported by the National Natural Science Foundation of China (10071058)Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.

STRONG LAW OF LARGE NUMBERS AND GROWTH RATE FOR NOD SEQUENCES

In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)and the strong law of large numbers and strong growth rate for negatively orthant dependent sequences.

Strong Law of Large Numbers under an Upper Probability

Strong law of large numbers is a fundamental theory in probability and statistics. When the measure tool is nonadditive, this law is very different from additive case. In 2010 Chen investigated the strong law of large numbers under upper probabilityVby assumingVis continuous. This assumption is very strong. Upper probabilities may not be continuous. In this paper we prove the strong law of large numbers for an upper probability without the continuity assumption whereby random variables are quasi-continuous and the upper probability is generated by a weakly compact family of probabilities on a complete and separable metric sample space.

On Strong Law of Large Numbers for Random Sequence

这笔记被奉献介绍有条件地统治的随机的变量的一个新概念。在下面合适限制条件，为任意的连续随机的变量的大数字的一条一般强壮的法律被获得。

Strong Law of Large Numbers for a 2-Dimensional Array of Pairwise Negatively Dependent Random Variables

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.

A note on strong law of large numbers of random variables

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.

The Sufficient and Necessary Conditions of the Strong Law of Large Numbers under Sub-linear Expectations

In this paper, by establishing a Borel–Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random variables on R^(∞) under a probability, we give the sufficient and necessary conditions of the strong law of large numbers for independent and identically distributed random variables under the sub-linear expectation, and the sufficient and necessary conditions for the convergence of an infinite series of independent random variables, without the assumption on the continuity of the capacities. A purely probabilistic proof of a weak law of large numbers is also given.

Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models

This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random variables.Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided.In particular,the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product.The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables.As an application,the authors investigate the errors-in-variables(EV,for short)regression models and establish the strong consistency for the least square estimators.Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.

Strong Law of Large Numbers and Asymptotic Equipartition Probability for Nonsymmetric Markov Chain Indexed by Cayley Tree

In this paper,we study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain（NSMC） indexed by Cayley tree with any finite states.The asymptotic equipartition properties with almost everywhere（a.e.） convergence for NSMC indexed by Cayley tree are obtained.This article generalizes a recent result.

A Remark on Strong Law of Large Numbers for Weighted U-Statistics

Let （X, Xn; n≥ 1} be a sequence of i.i.d, random variables with values in a measurable space （S,8） such that E｜h（X1, X2,..., Xm）｜ 〈 ∞, where h is a measurable symmetric function from Sm into R = （-∞, ∞）. Let {wn,i1,i2 im ; 1 ≤ i1 〈 i2 〈 …… 〈im 〈 n, n ≥ m} be a matrix array of real numbers. Motivated by a result of Choi and Sung （1987）, in this note we are concerned with establishing a strong law of large numbers for weighted U-statistics with kernel h of degree m. We show that whenever SUP n≥m max1〈i1〈i2〈…〈im≤｜wn i1,i2 i,im｜ 〈∞, where 0 = Eh（X1, X2,..., Xm）. The proof of this result is based on a new general result on complete convergence, which is a fundamental tool, for array of real-valued random variables under some mild conditions.

Strong law of large numbers for pair-wise extended lower/upper negatively dependent random variables

We establish some strong limit theorems for a sequence of pair-wise extended lower/upper negatively dependent random variables and give some new examples of dependent random variables.

Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree

In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree.

equivalent conditions of complete convergence for m-dimensional products of iid random variables and application to strong law of large numbers

Under very weak condition 0 【 r(t)↑∞ , t→∞. we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some results on strong law of large numbers are given such that our results are much stronger than the corresponding result of Gadidov’s.

THE STRONG LAW OF LARGE NUMBERS FOR PAIRWISE NQD RANDOM VARIABLES

在这份报纸，为 pairwise 的几乎肯定的集中否定地，象限依赖者随机变量被学习。为 pairwise 的大数字的强壮的法律否定地，象限依赖者随机变量被获得。我们的结果在 Marcinkiewicz (1937 ) 以前获得的定理， Jamison (1965 ) ， Matula (1992 ) 和从独立人士的吴(2001 ) 相等散布了的几乎肯定集中(i.i.d ) 上概括并且改善那些大小写到 pairwise NQD 序列。

Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence

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.