Weak Laws of Large Numbers for sequences of random variables with infinite rth moments

被引:0
作者
L. V. Dung
T. C. Son
N. T. H. Yen
机构
[1] Da Nang University of Education,
[2] Hanoi University of Science,undefined
来源
Acta Mathematica Hungarica | 2018年 / 156卷
关键词
infinite moment; weak law of large numbers; random variable; independence; limit theorem; weighted sum; 60F15; 60G50;
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摘要
Let (Xn;n≥1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(X_n;n \geq 1)}$$\end{document} be a sequence of independent random variables with infinite rth absolute moments for some 0<r<2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${0 < r < 2}$$\end{document}. We investigate weak laws of large numbers for the weighted sum Sn=∑j=1mncnjXj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S_n = \sum_{j=1}^{m_n}c_{nj}X_j}$$\end{document}, where (cnj;1≤j≤mn,n≥1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(c_{nj};1 \leq j \leq m_n,n \geq 1)}$$\end{document} is an array of real numbers. As illustrative examples, we obtain a weak law of large numbers of extended Pareto–Zipf distributions and generalized Feller Game. Furthermore, these results are applied to study weak law of large numbers of moving average sums of a sequence of i.i.d. random variables.
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页码:408 / 423
页数:15
相关论文
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