dc.contributor.author |
Al Hayek N. |
|
dc.contributor.author |
Ordóñez Cabrera M. |
|
dc.contributor.author |
Rosalsky A. |
|
dc.contributor.author |
Ünver M. |
|
dc.contributor.author |
Volodin A. |
|
dc.date.accessioned |
2022-02-09T20:30:46Z |
|
dc.date.available |
2022-02-09T20:30:46Z |
|
dc.date.issued |
2021 |
|
dc.identifier.issn |
0010-0757 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/168660 |
|
dc.description.abstract |
In this article, the concept of J-uniform integrability of a sequence of random variables { Xk} with respect to { ank} is introduced where J is a non-trivial ideal of subsets of the set of positive integers and { ank} is an array of real numbers. We show that this concept is weaker than the concept of { Xk} being uniformly integrable with respect to { ank} and is more general than the concept of B-statistical uniform integrability with respect to { ank}. We give two characterizations of J-uniform integrability with respect to { ank}. One of them is a de La Vallée Poussin type characterization. For a sequence of pairwise independent random variables { Xk} which is J-uniformly integrable with respect to { ank} , a law of large numbers with mean ideal convergence is proved. We also obtain a version without the pairwise independence assumption by strengthening other conditions. Supplements to the classical Mean Convergence Criterion are also established. |
|
dc.relation.ispartofseries |
Collectanea Mathematica |
|
dc.subject |
Mean convergence |
|
dc.subject |
Sequence of random variables |
|
dc.subject |
Summability methods |
|
dc.subject |
Uniform integrability |
|
dc.subject |
Weighted sums |
|
dc.title |
Some results concerning ideal and classical uniform integrability and mean convergence |
|
dc.type |
Article |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.source.id |
SCOPUS00100757-2021-SID85115091715 |
|