Complete moment convergence of moving average processes for $m$-widely acceptable sequence under sub-linear expectations

TL;DR

This paper establishes complete moment convergence for partial sums of moving average processes involving $m$-widely acceptable random variables under sub-linear expectations, extending classical probability results to this broader framework.

Contribution

It introduces the first complete moment convergence results for moving average processes with $m$-widely acceptable variables under sub-linear expectations.

Findings

Proves convergence under specific conditions on coefficients and variables.

Extends classical probability results to sub-linear expectation spaces.

Provides theoretical foundation for future research in this area.

Abstract

In this article, the complete moment convergence for the partial sum of moving average processes $\{X_n=\sum_{i=-\infty}^{\infty}a_iY_{i+n},n\ge 1\}$ is estabished under some proper conditions, where $\{Y_i,-\infty<i<\infty\}$ is a sequence of $m$-widely acceptable ($m$-WA) random variables, which is stochastically dominated by a random variable $Y$ in sub-linear expectations space $(\Omega,\HH,\ee)$ and $\{a_i,-\infty<i<\infty\}$ is an absolutely summable sequence of real numbers. The results extend the relevant results in probability space to those under sub-linear expectations.