RH-conservative matrix characterization of P-convergence in probability

Patterson R. F., Savaş E.

Computers and Mathematics with Applications, vol.63, no.6, pp.1020-1025, 2012 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 6
  • Publication Date: 2012
  • Doi Number: 10.1016/j.camwa.2011.10.057
  • Journal Name: Computers and Mathematics with Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1020-1025
  • Keywords: P-convergence in probability, P-convergent, Pringsheim limit point, Random variables, RH-conservative
  • Uşak University Affiliated: No

Abstract

The goal of this paper is to characterize P-convergence in probability of four-dimensional weighted means using RH-conservative matrices. We begin with the presentation of the following theorem. Let (Xk, l)=( XkXl) be a double sequence of non-degenerate independently identically distributed random variables such that E(Xk, l)=μ and E(Xk, l)<∞ for each (k,l). Suppose that A=(am, n,k,l) is an RH-conservative matrix; then the necessary and sufficient condition for Ym, n to P-converge to μ(a-∑ k,lck, l)+∑ k,lck, lXk, l in probability is that P-limm,nsupk,l|am, n,k,l-ck, l|=0. Other variations and implications will also be presented. © 2012 Published by Elsevier Ltd.