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Abstract <p>In this paper, we refine the mean convergence result of order <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8266_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="97" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\ (1\leq r&lt;2)\)</EquationSource> <!--LobJMat2560624Nguyen-m3--> </InlineEquation> for arrays of rowwise widely orthant dependent random variables. Specifically, we address an open problem posed by Thành (RACSAM 118(1): Paper No. 40, 2024), who suggested that his method could improve the result of Wu et al. (Stochastics <b>91</b> (6), 926–944 (2019)) by relaxing its restrictive assumptions. By applying Thành’s weaker criterion, we enhance the mean convergence result for arrays of rowwise widely orthant dependent random variables with general norming constants, thereby providing a significant refinement of Wu et al.’s findings.</p>

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Convergence in \(\boldsymbol{r}\)-Mean of Arrays of Rowwise Widely Orthant Dependent Random Variables

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Nguyen Ngoc Tu

摘要

Abstract

In this paper, we refine the mean convergence result of order \(r\ (1\leq r<2)\) for arrays of rowwise widely orthant dependent random variables. Specifically, we address an open problem posed by Thành (RACSAM 118(1): Paper No. 40, 2024), who suggested that his method could improve the result of Wu et al. (Stochastics 91 (6), 926–944 (2019)) by relaxing its restrictive assumptions. By applying Thành’s weaker criterion, we enhance the mean convergence result for arrays of rowwise widely orthant dependent random variables with general norming constants, thereby providing a significant refinement of Wu et al.’s findings.