Abstract
In this article, the complete moment convergence for the partial sum of moving average processes {X_{n}=sum_{i=-infty}^{infty}a_{i}Y_{i+n},ngeq 1} is established under some mild conditions, where {Y_{i},-infty < i<infty} is a doubly infinite sequence of random variables satisfying the Rosenthal type maximal inequality and {a_{i},-infty< i<infty} 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).
Highlights
We first introduce the definition of the Rosenthal type maximal inequality, which is one of the most interesting inequalities in probability theory and mathematical statistics
We refer to Shao [ ], Stoica [ ], Shen [ ], Yuan and An [ ] for negatively associated sequence (NA), martingale difference sequence, extended negatively dependent sequence (END), and asymptotically almost negatively associated random sequence (AANA), respectively
Suppose that {Xn, n ≥ } is a moving average process based on a sequence {Yi, –∞ < i < ∞} of identically distributed ρ-mixing random variables
Summary
We first introduce the definition of the Rosenthal type maximal inequality, which is one of the most interesting inequalities in probability theory and mathematical statistics. Li and Zhang [ ] established the following complete moment convergence of moving average processes under NA assumptions. The following complete moment convergence of moving average processes generated by ρ-mixing sequence was proved by Zhou and Lin [ ]. Suppose that {Xn, n ≥ } is a moving average process based on a sequence {Yi, –∞ < i < ∞} of identically distributed ρ-mixing random variables. Ko [ ] obtained the complete moment convergence of moving average processes generated by a class of random variable. For all ε > , The aim of this paper is to study the complete moment convergence of moving average process of random sequence under the assumption that the random variables satisfy the Rosenthal type maximal inequality and the weak mean dominating condition.
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