On P-convergence of four dimensional weighted sums of double random variables
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 ran...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia
2016
|
| Online Access: | http://journalarticle.ukm.my/9993/1/21%20RIchard%20F.%20Patterson.pdf http://journalarticle.ukm.my/9993/ http://www.ukm.my/jsm/english_journals/vol45num7_2016/contentsVol45num7_2016.html |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Universiti Kebangsaan Malaysia |
| Language: | English |
| id |
my-ukm.journal.9993 |
|---|---|
| record_format |
eprints |
| spelling |
my-ukm.journal.99932017-01-20T01:27:27Z http://journalarticle.ukm.my/9993/ On P-convergence of four dimensional weighted sums of double random variables Patterson, Richard F. Savas, Ekrem 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. Penerbit Universiti Kebangsaan Malaysia 2016-07 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/9993/1/21%20RIchard%20F.%20Patterson.pdf Patterson, Richard F. and Savas, Ekrem (2016) On P-convergence of four dimensional weighted sums of double random variables. Sains Malaysiana, 45 (7). pp. 1177-1181. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol45num7_2016/contentsVol45num7_2016.html |
| institution |
Universiti Kebangsaan Malaysia |
| building |
Perpustakaan Tun Sri Lanang Library |
| collection |
Institutional Repository |
| continent |
Asia |
| country |
Malaysia |
| content_provider |
Universiti Kebangsaan Malaysia |
| content_source |
UKM Journal Article Repository |
| url_provider |
http://journalarticle.ukm.my/ |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Patterson, Richard F. Savas, Ekrem |
| spellingShingle |
Patterson, Richard F. Savas, Ekrem On P-convergence of four dimensional weighted sums of double random variables |
| author_facet |
Patterson, Richard F. Savas, Ekrem |
| author_sort |
Patterson, Richard F. |
| title |
On P-convergence of four dimensional weighted sums
of double random variables |
| title_short |
On P-convergence of four dimensional weighted sums
of double random variables |
| title_full |
On P-convergence of four dimensional weighted sums
of double random variables |
| title_fullStr |
On P-convergence of four dimensional weighted sums
of double random variables |
| title_full_unstemmed |
On P-convergence of four dimensional weighted sums
of double random variables |
| title_sort |
on p-convergence of four dimensional weighted sums
of double random variables |
| publisher |
Penerbit Universiti Kebangsaan Malaysia |
| publishDate |
2016 |
| url |
http://journalarticle.ukm.my/9993/1/21%20RIchard%20F.%20Patterson.pdf http://journalarticle.ukm.my/9993/ http://www.ukm.my/jsm/english_journals/vol45num7_2016/contentsVol45num7_2016.html |
| _version_ |
1643737981099442176 |