Limiting behaviour of moving average processes genenrated by negatively dependent random variables under sub-linear expectations

TL;DR

This paper investigates the convergence properties of moving average processes generated by negatively dependent random variables under sub-linear expectations, extending classical results to a non-linear expectation framework.

Contribution

It establishes complete convergence and strong laws of large numbers for such processes under sub-linear expectations, complementing existing results under mixing conditions.

Findings

Proves complete convergence for moving average processes.

Establishes Marcinkiewicz-Zygmund strong law of large numbers.

Extends classical results to negatively dependent variables under sub-linear expectations.

Abstract

Let $\{Y_i,-\infty<i<\infty\}$ be a doubly infinite sequence of identically distributed, negatively dependent random variables under sub-linear expectations, $\{a_i,-\infty<i<\infty\}$ be an absolutely summable sequence of real numbers. In this article, we study complete convergence and Marcinkiewicz-Zygmund strog law of large numbers for the partial sums of moving average processes $\{X_n=\sum_{i=-\infty}^{\infty}a_{i}Y_{i+n},n\ge 1\}$ based on the sequence $\{Y_i,-\infty<i<\infty\}$ of identically distributed, negatively dependent random variables under sub-linear expectations, complementing the result of [Chen, et al., 2009. Limiting behaviour of moving average processes under $\varphi$-mixing assumption. Statist. Probab. Lett. 79, 105-111].