On the complete moment convergence of moving average processes generated by negatively dependent random variables under sub-linear expectations

Abstract

The moving average processes $ X_k = \sum_{i = -\infty}^{\infty}a_{i+k}Y_{i} $ are studied, where $ \{Y_i, -\infty < i < \infty\} $ is a double infinite sequence of negatively dependent random variables under sub-linear expectations, and $ \{a_i, -\infty < i < \infty\} $ is an absolutely summable sequence of real numbers. We establish the complete moment convergence of a moving average process under proper conditions, extending the corresponding results in classic probability space to those in sub-linear expectation space.

Keywords

• moving average process
• complete moment convergence
• weighted sums
• negatively dependent random variables
• sub-linear expectations