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 $\{X_n=\sum_{i=-\infty}^{\infty}a_iY_{i+n},n\ge 1\}$ 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 $(Ω,\HH,\ee)$ 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.

Theorems & Definitions (11)

• Definition 2.1
• Definition 2.2
• Definition 2.3
• Definition 2.4
• Lemma 2.1
• Lemma 2.2
• Lemma 2.3
• Lemma 2.4
• Theorem 3.1
• Theorem 3.2