Complete convergence of moving average processes produced by negatively dependent random variables under sub-linear expectations

Abstract

Suppose that $ \{a_i, -\infty < i < \infty\} $ is an absolutely summable set of real numbers, $ \{Y_i, -\infty < i < \infty\} $ is a subset of identically distributed, negatively dependent random variables under sub-linear expectations. Here, we get complete convergence and Marcinkiewicz-Zygmund strong 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\} $ produced by $ \{Y_i, -\infty < i < \infty\} $ of identically distributed, negatively dependent random variables under sub-linear expectations, complementing the relevant results in probability space.

Keywords

• complete moment convergence
• complete convergence
• negatively dependent random variables
• sub-linear expectations