Note on the complete moment convergence for moving average process of a class of random variables under sub-linear expectations

Abstract

In this paper, the complete moment convergence for the partial sums of moving average processes $\{X_n=\sum_{i=-\infty}^{\infty}a_iY_{i+n},n\ge 1\}$ is proved under some proper conditions, where $\{Y_i,-\infty<i<\infty\}$ is a doubly sequence of identically distributed, negatively dependent random variables under sub-linear expectations and $\{a_i,-\infty<i<\infty\}$ is an absolutely summable sequence of real numbers. The results established in sub-linear expectation spaces generalize the corresponding ones in probability space.

Theorems & Definitions (11)

• Definition 2.1
• Definition 2.2
• Lemma 2.1
• Theorem 3.1
• Remark 3.1
• Remark 3.2
• Remark 3.3
• Theorem 3.2
• Remark 3.4
• proof : Proof of Theorem \ref{['thm2.1']}