A generalization of almost sure local limit theorem of uniform empirical process

被引：0
作者：
Chenglian Zhu
机构：
[1] Huaiyin Normal University,School of Mathematical Science
来源：
Journal of Inequalities and Applications | / 2015卷
关键词：
almost sure central limit theorem; almost sure local central limit theorem; uniform empirical process; 60E15; 60F15;
D O I：
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学科分类号：
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}$\{X_{n}; n\geq1\}$\end{document} be a sequence of independent and identically distributed U[0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$U[0, 1]$\end{document}-distributed random variables. In this paper, we are concerned with the almost sure local central limit theorem of ∥Fn∥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\|F_{n}\|$\end{document} and sup0≤t≤1Fn(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sup_{0\leq t\leq1}F_{n}(t)$\end{document}, and some corresponding results are derived.
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