Mathematics

CLC number: O211.6

Complete Convergence for Moving Average Processes under m-WOD Random Variables

m-宽相依随机变量序列移动平均过程的收敛性

Department of Mathematics and Computer Science, Tongling University, Tongling 244000, Anhui, China

Received: 27 November 2023

Abstract

The m-widely orthant dependent (m-WOD) sequences are very weak dependent random variables. In the paper, the authors investigate the moving average processes, which is generated by m-WOD random variables. By using the tail cut technique and maximum moment inequality of the m-WOD random variables, moment complete convergence and complete convergence of the maximal partial sums for the moving average processes are obtained, the results generalize and improve some corresponding results of the existing literature.

摘要

m-宽相依随机变量序列(m-WOD)是非常宽泛的相依随机变量序列。本文主要研究m-WOD随机变量序列生成的移动平均过程的收敛性，通过采用随机变量尾截的方法和m-WOD序列矩不等式，获得了该移动平均过程最大部分和的矩完全收敛性和完全收敛性，获得的成果推广了现有文献中的一些相应结果。