Title

RH-conservative matrix characterization of P-convergence in probability

Document Type

Article

Publication Date

3-1-2012

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.

Publication Title

Computers and Mathematics with Applications

Volume

63

Issue

6

First Page

1020

Last Page

1025

Digital Object Identifier (DOI)

10.1016/j.camwa.2011.10.057

ISSN

08981221

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