Complete moment convergence of pairwise NQD random variables

It is known that the dependence structure of pairwise negative quadrant dependent (NQD) random variables is weaker than those of negatively associated random variables and negatively orthant dependent random variables. In this article, we investigate the moving average process which is based on the pairwise NQD random variables. The complete moment convergence and the integrability of the supremum are presented for this moving average process. The results imply complete convergence and the Marcinkiewicz–Zygmund-type strong law of large numbers for pairwise NQD sequences.     

Complete moment convergence for arrays of rowwise NSD random variables

In this paper, the complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are investigated. Some sufficient conditions to prove the complete convergence and the complete moment convergence are presented. The results obtained in the paper generalize and improve some corresponding ones for independent random variables and negatively associated random variables.     

NA随机变量阵列的完全矩收敛性

利用NA随机变量的矩不等式和截尾方法,研究了NA随机变量阵列的完全矩收敛性,给出了证明NA随机变量阵列完全矩收敛性的一些充分条件.所得结果推广了已有文献关于NA随机变量的相应结果.     

ND阵列加权乘积和的完全收敛性

设（Xni：1≤i≤n,n≥1）为行间ND阵列,g（x）是R^＋上指数为α的正则变化函数,{αni：1≤i≤n,n≥1}为满足条件max1≤i≤n｜ani｜=0（（g（n））^-1）的实数阵列．本文采用截尾的方法,得到了使ND随机变量阵列加权乘积和完全收敛的条件,并推广了以前学者的结论．     

Complete moment convergence for i.i.d. random variables

In the paper, the complete moment convergence is obtained for i.i.d. random variables such that all moments exist, but the moment generating function does not exist. The main results extend the related known works due to Gut and Stadtmüller.     

Complete moment and integral convergence for sums of negatively associated random variables

For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE（max1≤k≤n｜Sk｜^1/q-∈bn^1/qp）^＋〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 （log n） ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.     

NOD随机变量序列加权和的矩完全收敛性

讨论了NOD随机变量序列加权和的矩完全收敛性,获得了NOD随机变量序列加权和的矩完全收敛性的充要条件.这些结论显示了矩完全收敛性和矩条件之间的等价关系,同时推广了Wu Qunying(2011)的结果.     

Complete and complete moment convergence for weighted sums of widely orthant dependent random variables

In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature.     

行为NSD随机变量阵列加权和的q阶矩完全收敛性

利用Hoffmann-Jφrgensen型概率不等式和截尾法,获得了行为NSD随机变量阵列加权和的q阶矩完全收敛性的充分条件.利用这些充分条件,不仅推广和深化梁汉营等(2010)和郭明乐等(2014)的结论,而且使他们的证明过程得到了极大地简化.     

Complete convergence for weighted sums of LNQD random variables

In this paper, we study the complete convergence for weighted sums of linearly negative quadrant dependent (LNQD) random variables based on the exponential bounds. In addition, we present some complete convergence for arrays of rowwise LNQD random variables.     

Complete convergence for randomly indexed sums of random variables

The complete convergence of normed sums of independent identically distributed random variables with random indices is studied. Some applications for subsequences and sequences with multidimensional indices are given. Supported by the Hungarian Foundation for Scientific Research (grant OTKA-1650/1991). Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994.     

The laws of large numbers for Pareto-type random variables under sub-linear expectation

In this paper, some laws of large numbers are established for random variables that satisfy the Pareto distribution, so that the relevant conclusions in the traditional probability space are extended to the sub-linear expectation space. Based on the Pareto distribution, we obtain the weak law of large numbers and strong law of large numbers of the weighted sum of some independent random variable sequences.     

非同分布NA序列的完全收敛性

讨论了非同分布NA序列部分和与随机足标部分和的完全收敛性，推广了于浩在1989年得到的关于独立随机变量序列的一些结果。     

Complete moment convergence for weighted sums of widely orthant-dependent random variables and its application in nonparametric regression models

We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent (WOD) random variables, which improve and extend the corresponding results of Y. F. Wu, M. G. Zhai, and J. Y. Peng [J. Math. Inequal., 2019, 13(1): 251–260]. As an application of the main results, we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.     

WOD随机变量加权和的完全收敛性

宽象限相依变量(简称WOD变量)是一类包含独立变量,负相协变量(简称NA变量),负象限相依变量(简称NOD变量)和推广的负象限相依变量(简称END变量)在内的非常广泛的相依变量.本文利用WOD变量的Rosenthal型矩不等式和随机变量的截尾技术,在一般的条件下建立了WOD变量加权和的完全收敛性.所得结果推广了若干相依变量的相应结果.     

Complete convergence and almost sure convergence of weighted sums of random variables

Letr>1. For eachn1, let {X _nk , –<k<} be a sequence of independent real random variables. We provide some very relaxed conditions which will guarantee for every >0. This result is used to establish some results on complete convergence for weighted sums of independent random variables. The main idea is that we devise an effetive way of combining a certain maximal inequality of Hoffmann-Jørgensen and rates of convergence in the Weak Law of Large Numbers to establish results on complete convergence of weighted sums of independent random variables. New results as well as simple new proofs of known ones illustrate the usefulness of our method in this context. We show further that this approach can be used in the study of almost sure convergence for weighted sums of independent random variables. Convergence rates in the almost sure convergence of some summability methods ofiid random variables are also established.     

Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

In this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive.     

Lindeberg's central limit theorems for martingale-like sequences under sub-linear expectations

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes, especially stochastic integrals and differential equations. In this paper, the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation. As applications, the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables, and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given. For proving the results, Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.     

A note on the convergence of sequences of conditional expectations of random variables

Summary We disprove two theorems on the convergence of sequences of conditional expectations of random variables in [1] by providing a counterexample.     

NOD随机变量阵列加权乘积和的完全收敛性

利用NOD随机变量的性质,研究了行为NOD随机变量阵列加权乘积和的完全收敛性,获得了一些新的结果,所得的结果推广和改进了已知的一些文献中的一系列结果.