Further research on complete moment convergence for moving average process of a class of random variables

摘要

In this article, the complete moment convergence for the partial sum of moving average processes { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } ${X_{n}=sum_{i=-infty}^{infty}a_{i}Y_{i+n},ngeq 1}$ is established under some mild conditions, where { Y i , − ∞ i ∞ } ${Y_{i},-infty iinfty}$ is a doubly infinite sequence of random variables satisfying the Rosenthal type maximal inequality and { a i , − ∞ i ∞ } ${a_{i},-infty iinfty}$ is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results given by Ko (J. Inequal. Appl. 2015:225, 2015).