一类非齐次树上的Shannon-McMillan定理

通过构造适当的辅助鞅差序列,利用鞅差序列的收敛定理给出了一类特殊非齐次树上具有a.e.收敛性质的Shannon-M cM illan定理.     

A general central limit theorem for strong mixing sequences

A central limit theorem for strong mixing sequences is given that applies to both non-stationary sequences and triangular array settings. The result improves on an earlier central limit theorem for this type of dependence given by Politis, Romano and Wolf in 1997.     

多维随机向量序列加权和的中心极限定理

本文研究了多维随机向量序列加权和的渐近行为.利用Lindeberg中心极限定理的基本思想,得到了多维随机向量序列加权和的中心极限定理及其收敛速度,为Lindeberg中心极限定理的推广.     

An almost sure central limit theorem for the weight function sequences of NA random variables

Consider the weight function sequences of NA random variables. This paper proves that the almost sure central limit theorem holds for the weight function sequences of NA random variables. Our results generalize and improve those on the almost sure central limit theorem previously obtained from the i.i.d. case to NA sequences.     

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-Jorgensen and Pisier theorem are obtained.     

Convergence of processes of step sums on mixing processes

We prove a limit theorem on the convergence of nonhomogeneous centered processes of step sums, constructed on random mixing sequences, to a process with independent increments. We also prove a invariance-principle type theorem for schemes of summation of functionals on random mixing sequences.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 716–721, May, 1990.     

Law of iterated logarithm for NA sequences with non-identical distributions

Based on a law of the iterated logarithm for independent random variables sequences, an iterated logarithm theorem for NA sequences with non-identical distributions is obtained. The proof is based on a Kolmogrov-type exponential inequality.     

任意随机序列级数的强收敛性

利用鞅差序列级数收敛定理研究任意随机序列级数的强收敛性,得到了该序列的一个强极限定理,某些经典的鞅差序列和独立随机变量序列的强极限定理是其特例.     

On Applications of Quasi-Monotone Sequences and Quasi Power Increasing Sequences

In this article, we prove a general theorem dealing with an application of quasi-f-power increasing sequences and δ-quasi monotone sequences. This theorem also includes some known and new results.     

Successively iterative method of nonlinear Neumann boundary value problems

Two successively iterative sequences are constructed for computing solutions of the nonlinear Neumann boundary value problems with time singularity. The sequences start off with some constants. Main tool is the fixed point theorem of increasing operator on the order interval. By considering convergence of the sequences, we prove the existence of nontrivial sign-changing solutions.     

任意随机变量序列的一个强极限定理

研究任意随机变量序列的强收敛性.利用鞅差序列级数收敛定理,证明了任意随机序列的一个强极限定理,作为推论,得到了马氏过程、鞅差序列及独立随机变量序列的强大数定律.     

任意随机变量序列级数的强收敛性

利用鞅差序列级数的收敛定理和条件三级数定理研究了任意随机变量序列级数的强收敛性,推广了某些经典的鞅差序列和独立随机变量序列及两两NQD序列的强极限定理.     

On the boundedness of Lagrange multipliers of the Kuhn-Tucker theorem applied to the problem of Tikhonov function minimization

In the proof of the convergence of sequences of approximations derived by the regularized method of linearization, the Kuhn-Tucker theorem with bounded sequences of Lagrange multipliers is applied to sequences of Tikhonov functions. This paper demonstrates that in the case of three existing forms of constrains: (i) functional inequalities strict at some point, (ii) linear functional inequalities, and (iii) a linear operator equality, there exist bounded sequences of Lagrange multipliers of the Kuhn-Thucker theorem applied to the sequences of Tikhonov functions.     

Central limit theorems under weak dependence

This article is motivated by a central limit theorem of Ibragimov for strictly stationary random sequences satisfying a mixing condition based on maximal correlations. Here we show that the mixing condition can be weakened slightly, and construct a class of stationary random sequences covered by the new version of the theorem but not Ibragimov's original version. Ibragimov's theorem is also extended to triangular arrays of random variables, and this is applied to some kernel-type estimates of probability density.     

A strong limit theorem on gambling systems

A strong limit theorem on gambling system for Bernoulli sequences is extended to the sequences of arbitrary discrete random variables by using the conditional probabilities. Furthermore, by allowing the selection function to take values in an interval, the conception of random selection is generalized. In the proof an approach of applying the differentiation of measure on a net to the investigation of the strong limit theorem is proposed.     

A von Neumann theorem for uniformly distributed sequences of partitions

In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann’s theorem on permutations of dense sequences and uniformly distributed sequences of points.     

On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales

We prove a theorem on the strong law of large numbers for martingales. The existence of higher moments is not assumed. From the theorem proved, we deduce numerous well-known results on the strong law of large numbers both for martingales and for sequences of sums of independent random variables.     

Applications of a binoomial-type identity

A generalization of the binomial theorem is proved for sequences of polynomials of binomial type. The equivalence of two formulas which count group-invariant partitions is shown to be a consequence of this theorem. The theorem is also used to demonstrate the equivalence of two formulas for rook polynomials.     

关于公平赌博的一个强极限定理

本文就较一般的情况引进公平赌博的概念,将关于Bernoulli序列赌博策略的一个强极限定理推广到取有限个值的相依变量的情况,并通过允许选择函数在一个区间中取值,推广了随机选择的概念.证明中提出了将测度的网微分法和条件母函数的工具应用于赌博系统强极限定理的研究的一种途径.