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

Abstract

In this article, the complete moment convergence for the partial sum of moving average processes $\{X_n={\sum }_{i=-\infty }^{\infty }{a}_i{Y}_{i+n},n\ge 1\}$ 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 $(Ω,\HH,\ee)$ 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.

16 pages,submitted to Journal of Inequalities and Applications