RH-conservative matrix characterization of P-convergence in probability
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.
Computers and Mathematics with Applications
Digital Object Identifier (DOI)
Patterson, & Savaş, E. (2012). RH-conservative matrix characterization of P-convergence in probability. Computers & Mathematics with Applications, 63(6), 1020–1025. https://doi.org/10.1016/j.camwa.2011.10.057