An extension on the rate of complete moment convergence for weighted sums of weakly dependent random variables

Haiwu Huang; Yuan Yuan; Hongguo Zeng; Haiwu Huang; Yuan Yuan; Hongguo Zeng

doi:10.3934/math.2023029

AIMS Mathematics

2023, Volume 8, Issue 1: 622-632. doi: 10.3934/math.2023029

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Research article

An extension on the rate of complete moment convergence for weighted sums of weakly dependent random variables

1.
School of Science, Guilin University of Aerospace Technology, Guilin 541004, China
2.
Library, Guilin University of Aerospace Technology, Guilin 541004, China

Received: 28 June 2022 Revised: 31 August 2022 Accepted: 02 September 2022 Published: 09 October 2022
MSC : 60F15

The authors study the convergence rate of complete moment convergence for weighted sums of weakly dependent random variables without assumptions of identical distribution. Under the moment condition of $ E{{{\left| X \right|}^{\alpha }}}/{{{\left(\log \left(1+\left| X \right| \right) \right)}^{\alpha /\gamma -1}}}\; < \infty $ for $ 0 < \gamma < \alpha $ with $ 1 < \alpha \le 2 $, we establish the complete $ \alpha $-th moment convergence theorem for weighted sums of weakly dependent cases, which improves and extends the related known results in the literature.
- complete $ \alpha $-th moment convergence,
- weakly dependent random variables,
- weighted sums
Citation: Haiwu Huang, Yuan Yuan, Hongguo Zeng. An extension on the rate of complete moment convergence for weighted sums of weakly dependent random variables[J]. AIMS Mathematics, 2023, 8(1): 622-632. doi: 10.3934/math.2023029

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Abstract

The authors study the convergence rate of complete moment convergence for weighted sums of weakly dependent random variables without assumptions of identical distribution. Under the moment condition of $ E{{{\left| X \right|}^{\alpha }}}/{{{\left(\log \left(1+\left| X \right| \right) \right)}^{\alpha /\gamma -1}}}\; < \infty $ for $ 0 < \gamma < \alpha $ with $ 1 < \alpha \le 2 $, we establish the complete $ \alpha $-th moment convergence theorem for weighted sums of weakly dependent cases, which improves and extends the related known results in the literature.

References

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