Электронный архив

Some results concerning ideal and classical uniform integrability and mean convergence

Показать сокращенную информацию

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


Файлы в этом документе

Данный элемент включен в следующие коллекции

  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

Показать сокращенную информацию

Поиск в электронном архиве


Расширенный поиск

Просмотр

Моя учетная запись

Статистика