Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions

We obtain precise constants in the Marcinkiewicz-Zygmund inequality for martingales in for p>2 and a new Rosenthal type inequality for stationary martingale differences for p in ]2,3]. The Rosenthal inequality is then extended to stationary and adapted sequences. As in Peligrad et al. (Proc. Am. Math. Soc. 135:541–550, [2007]), the bounds are expressed in terms of -norms of conditional expectations with respect to an increasing field of sigma algebras. Some applications to a particular Markov chain are given.      

Almost-Sure Results for a Class of Dependent Random Variables

The aim of this note is to establish almost-sure Marcinkiewicz-Zygmund type results for a class of random variables indexed by _d ⁺ —the positive d-dimensional lattice points—and having maximal coefficient of correlation strictly smaller than 1. The class of applications include filters of certain Gaussian sequences and Markov processes.     

对称随机变量部分和的概率不等式

在对称随机变量分布函数关于原点的值大于或等于二分之一的基础上,阐明对称随机变量的部分和仍是对称随机变量,进一步,给出关于对称随机变量序列部分和的概率不等式.     

Rates in the Empirical Central Limit Theorem for Stationary Weakly Dependent Random Fields

A weak dependence condition is derived as the natural generalization to random fields on notions developed in Doukhan and Louhichi (1999). Examples of such weakly dependent fields are defined. In the context of a weak dependence coefficient series with arithmetic or geometric decay, we give explicit bounds in Prohorov metric for the convergence in the empirical central limit theorem. For random fields indexed by &Zopf ^d , in the geometric decay case, rates have the form n ^−1/(8d+24) L(n), where L(n) is a power of log(n). This revised version was published online in June 2006 with corrections to the Cover Date.     

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Strong laws of large numbers play key role in nonadditive probability theory. Recently, there are many research papers about strong laws of large numbers for independently and identically distributed (or negatively dependent) random variables in the framework of nonadditive probabilities (or nonlinear expectations). This paper introduces a concept of weakly negatively dependent random variables and investigates the properties of such kind of random variables under aframework of nonadditive probabilities and sublinear expectations. A strong law of large numbers is also proved for weakly negatively dependent random variables under a kind of sublinear expectation as an application     

Weighted Invariance Principle for Banach Space-Valued Random Variables

A weighted weak invariance principle for nonseparable Banach space-valued functions is described via asymptotic behavior of a weighted Wiener process. It is proved that, unlike the usual weak invariance principle, the weighted variant cannot be characterized via validity of a central limit theorem in a Banach space. A strong invariance principle is introduced in the present context and used to prove the weighted weak invariance principle that we seek herewith. The result then is applied to empirical processes.     

Some New Results on Covariances Involving Order Statistics from Dependent Random Variables

Formulas for covariance matrix between a random vector and its ordered components are derived for different distributions including multivariate normal,t, andF. The present formulas and related results obtained here lead to some known results in the literature as special cases.     

Maximum of partial sums and an invariance principle for a class of weak dependent random variables

The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle and the convergence of the moments in the central limit theorem.

     

On the Law of Large Numbers for Weakly Dependent Random Variables

In this paper, we present the Hsu–Robbins and Spitzer law of large numbers for m-dependent and -mixing random variables. In the main theorems, we do not assume that the random variables are identically distributed.     

负相依随机变量之和的概率大偏差不等式

本文建立了负相依随机变量序列的概率大偏差不等式，并推广了以往文献的结果．