Strong Laws of Large Numbers for Weighted Sums of Hilbert-valued Coordinatewise PNQD Random Variables with Applications

Abstract

The aim of this paper is to investigate results on almost sure convergence of weighted sums of coordinatewise pairwise negatively quadrant dependent random variables taking values in Hilbert spaces. As an application, the almost sure convergence of degenerate von Mises-statistics is investigated. Keywords: Negative quadrant dependence, Hilbert spaces, Weighted sums, Strong laws of large numbers.