Complete moment convergence for randomly weighted sums of arrays of rowwise mndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$m_n$$end{document}-extended negatively dependent random variables and its applications

摘要

Abstract In this paper, a new concept of rowwise mndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$m_n$$end{document}-extended negatively dependent (rowwise mndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$m_n$$end{document}-END) random variables, which is wider than some known dependent structures such as END, widely orthant dependence (WOD) and so on, is introduced, and complete moment convergence for randomly weighted sums of rowwise mndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$m_n$$end{document}-END arrays are investigated under some proper and sufficient conditions. In addition, a relationship between {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}$${m_n,nge 1}$$end{document}, dominating sequence and moment conditions for convergence is in a sense revealed. The results obtained in the paper generalise some corresponding ones for independent and some dependent random variables. As applications, strong convergence for elements of a linear autoregression model and complete convergence for randomly indexed sums of sequences of WOD random variables are established.