A strong law of large numbers for fuzzy random variables

A limit of a sequence of fuzzy numbers is defined and its some properties are shown. Based on these concept and properties, an independent sequence of fuzzy random variables is considered and a strong law of large numbers for fuzzy random variables is shown.     

关于任意离散随机序列的一个强偏差定理

引用极限对数似然比的概念作为任意随机序列联合分布与其边缘分布"不相似性"的度量,构造几乎处处收敛的上鞅,讨论了任意离散随机序列的强偏差定理.     

N值随机序列的随机选择的强极限定理

将赌博系统的随机选择理论扩展到N值随机序列,利用似然比概念及分析技术,得到一个随机选择下有序数偶相对频率的强极限定理     

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.     

Kolmogorov's strong law of large numbers for fuzzy random variables

In this paper, Kolmogorov's strong law of large numbers for sums of independent and level-wise identically distributed fuzzy random variables is obtained.     

Inequalities and strong laws of large numbers for random allocations

Summary Moment inqualities and strong laws of large numbers are proved for random allocations of balls into boxes. Random broken lines and random step lines are constructed using partial sums of i.i.d. random variables that are modified by random allocations. Functional limit theorems for such random processes are obtained.     

On the strong limit theorems for double arrays of blockwise M-dependent random variables

For a double array of blockwise M-dependent random variables {X _mn ,m ?? 1, n ?? 1}, strong laws of large numbers are established for double sums ?? _i=1 ^m ?? _j=1 ⁿ X _ij , m ?? 1, n ?? 1. The main results are obtained for (i) random variables {X _mn ,m ?? 1, n ?? 1} being non-identically distributed but satisfy a condition on the summability condition for the moments and (ii) random variables {X _mn ,m ?? 1, n ?? 1} being stochastically dominated. The result in Case (i) generalizes the main result of Móricz et al. [J. Theoret. Probab., 21, 660?C671 (2008)] from dyadic to arbitrary blocks, whereas the result in Case (ii) extends a result of Gut [Ann. Probab., 6, 469?C482 (1978)] to the bockwise M-dependent setting. The sharpness of the results is illustrated by some examples.     

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.     

The strong law of large numbers for pairwise negatively dependent random variables

Necessary and sufficient conditions for the validity of the strong law of large numbers for pairwise negatively dependent random variables with infinite means are formulated.     

On complete convergence for strong mixing sequences

In this paper, some results on complete convergence for strong mixing sequences are presented under some suitable conditions. A Marcinkiewicz–Zygmund-type strong law of large numbers is also obtained.     

一类强大数定律的推广

设Ｘｎ（ｎ≥０）是在可数集Ｅｎ中取值的随机变量，Ａｎ（ｘ０，…，ｘｎ－１）是定义在Ｅ０×…×Ｅｎ－１上的正值函数，｛φｎ（ｘ），ｎ≥１｝是（－∞，＋∞）上的正值连续偶函数序列，且当｜ｘ｜增加时，φｎ（ｘ）／｜ｘ｜↑，φｎ（ｘ）／ｘ２↓．本文给出了ａ．ｅ．收敛的一个充分条件．所得结果是一类经典强大数定律的推广．证明中发展了第一作者所提出的研究离散随机变量序列强极限定理的分析方法．     

A central limit theorem for random sums of random variables

Anscombe (1952) (also see Chung (1974)) has developed a central limit theoremof random sums of independent and identically distributed random variables. Applicability of this theorem in practice, however, is limited since the normalization requires random factors. In this paper we establish sufficient conditions under which the central limit theorem holds when such random factors are replaced by the underlying asymptotic mean and standard ddeviation. An application of this result in the context of shock models is also given.     

A local limit theorem for independent random variables

A local limit theorem is given for independent noninteger random variables under a condition which is more general than one previously given, and which reduces, in the case of identically distributed random variables, to a well-known result.     

An analog of the Baum-Katz theorem for weakly dependent random variables

In this paper we study the limiting behavior of sums of dependent random variables under a strong mixing condition. We obtain conditions for which an analog of the Baum-Katz theorem holds and cite an example showing their optimality. Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 360–368, March, 2000.     

Asymptotic behavior for random walk in random environment with holding times

In this article, we mainly discuss the asymptotic behavior for multi-dimensional continuous-time random walk in random environment with holding times. By constructing a renewal structure and using the point “environment viewed from the particle”, under General Kalikow's Condition, we show the law of large numbers (LLN) and central limit theorem (CLT) for the escape speed of random walk.     

Strong limit theorems for arbitrary stochastic sequences

In this paper, we establish two strong limit theorems for arbitrary stochastic sequences. As corollaries, we generalize some known results.     

Strong convergence for sequences of asymptotically almost negatively associated random variables

In this article, the complete convergence for sequences of asymptotically almost negatively associated (AANA) random variables is studied. As applications, the Baum–Katz-type theorem, Hsu–Robbins-type theorem and Marcinkiewicz–Zygmund strong law of large numbers for sequences of AANA random variables are obtained.     

One-sided limit theorems for sums of multidimensional indexed random variables

Let {X,X _n,nZ ₊ ^d } be a sequence of independent and identically distributed random variables and {a _n ,n Z ₊ ^d } be a sequence of constants. We examine the almost sure limiting behavior of weighted partial sums of the form _|n|N a _n X _n . Suppose further that eitherEX=0 orE|X|=. In most situations these normalized partial sums fail to have a limit, no matter which normalizing sequence we choose. Thus, the investigation lends itself to the study of the limit inferior and limit superior of these sequences. On the way to proving results of this type we first establish several weak laws. These weak laws prove to be of great value in establishing generalized laws of the iterated logarithm.     

Exponential inequalities for associated random variables and strong laws of large numbers

Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately.