Sains Malaysiana 45(7)(2016): 1177–1181
On P-Convergence of Four Dimensional Weighted
Sums of Double Random Variables
(Hasil Tambah Berpemberat Empat Dimensi Berganda
Pemboleh Ubah
Rawak ke atas
Penumpuan-P)
RICHARD F.
PATTERSON1
& EKREM SAVAS2*
1Department of Mathematics
and Statistics, University of North Florida Jacksonville
Florida, 32224, USA
2Department of Mathematics,
Istanbul Ticaret University, Sutluce-Istanbul, Turkey
Diserahkan: 6 Oktober 2015/Diterima:
19 Disember 2015
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 [xk,l] be a double sequence of pairwise
independent random variables such that [xk, l]
was uniformly integrable. Let [am,
n, k, l] be a four dimensional matrix such
that ≤ C for all ordered pair (m, n) and
for some C and converges to 0 in probability. Then (xk,l –
E(xk,l) converges in mean
to 0. Other extensions and variations via multidimensional
transformation shall also be presented.
Keywords: Double sequences
Pringsheim limit point; P-convergent; RH-Regular
ABSTRAK
Penyelidikan ini bertujuan untuk
membentangkan satu
siri teorem had yang mencirikan pemboleh ubah rawak bebas
berganda melalui
keterhasiltambahan transformasi
empat dimensi. Untuk mencapai matlamat ini, kami mulakan dengan memberikan teorem yang mencirikan pasangan demi pasangan pemboleh ubah rawak: biar
[xk,l]
menjadi jujukan
ganda dua pasangan
demi pasangan pemboleh
ubah rawak bebas
supaya [xk, l]
menjadi seragam
terkamir. Biar [am,
n, k, l] menjadi
empat dimensi matriks
supaya
≤
C untuk semua
pasangan yang disusun (m,
n) dan bagi
sesetengah C dan penumpuan dalam kebarangkalian kepada 0. Kemudian (xk,l –
E(xk,l) menumpu
pada min untuk
0. Perluasan lain dan
variasi melalui
transformasi bermultimatra turut dikemukakan.
Kata kunci: Jujukan
ganda dua titik had Pringsheim; penumpuan P; RH biasa
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*Pengarang untuk surat-menyurat; email: ekremsavas@yahoo.com
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