On P-convergence of four dimensional weighted sums of double random variables
Document Type
Article
Publication Date
7-1-2016
Abstract
The goal of this paper was to present a series of limit theorems that characterizes independent double random variables via four dimensional summability transformation. In order to accomplish this goal we began with the presentation of the following theorem that characterize pairwise independent random variables: let [xκ,l] be a double sequence of pairwise independent random variables such that [xκ,l] was uniformly integrable. Let [am, n, k, l] be a four dimensional matrix such that (equation presented) ≤ C for all ordered pair (m, n) and for some C and (equation presented) converges to 0 in probability Then (equation presented) (xκ,l E(xκ,l) converges in mean to 0. Other extensions and variations via multidimensional transformation shall also be presented.
Publication Title
Sains Malaysiana
Volume
45
Issue
7
First Page
1177
Last Page
1181
ISSN
01266039
Citation Information
Patterson, R.F., & Savaş, E. (2016). On P-convergence of four dimensional weighted sums of double random variables. Sains Malaysiana, 45(7), 1177-1181.