The strong convergence properties of weighted sums for a class of dependent random variables

Song, Meimei; Zhu, Quanxin

doi:10.1080/03610926.2019.1589516

Cited by 2 publications

(1 citation statement)

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“…The limit properties of the moving average process {X n , n ≥ 1} have been extensively investigated by many authors. For example, Burton and Dehling [1] obtained a large deviation principle, Ibragimov [2] established the central limit theorem, Račkauskas and Suquet [3] proved the functional central limit theorems for self-normalized partial sums of linear processes, and An [4], Chen et al [5], Kim and Ko [6], Li et al [7], Li and Zhang [8], Wang and Hu [9], Yang and Hu [10], Zhang [11], Zhou [12], Zhou and Lin [13], Zhang [14], Zhang and Ding [15], Song and Zhu [16,17] got the complete (moment) convergence of moving average process based on a sequence of different dependent (or mixing) random variables, respectively. But few results for moving average process based on m-WOD random variables are known.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Complete moment convergence of moving average processes for m-WOD sequence

2021

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In this paper, the complete moment convergence for the partial sum of moving average processes $\{X_{n}=\sum_{i=-\infty }^{\infty }a_{i}Y_{i+n},n\geq 1\}$ { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } is established under some mild conditions, where $\{Y_{i},-\infty < i<\infty \}$ { Y i , − ∞ < i < ∞ } is a sequence of m-widely orthant dependent (m-WOD, for short) random variables which is stochastically dominated by a random variable Y, and $\{a_{i},-\infty < i<\infty \}$ { a i , − ∞ < i < ∞ } is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results from m-extended negatively dependent (m-END, for short) sequences to m-WOD sequences.

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