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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 1, Pages 115–133
DOI: https://doi.org/10.4213/tvp5398 (Mi tvp5398) 		 
This article is cited in 1 scientific paper (total in 1 paper)

A new version of uniform integrability via power series summability methods

M. Ordóñez Cabreraa, A. Rosalskyb, M. Ünverc, A. Volodind

a Department of Mathematical Analysis, University of Sevilla, Spain
b Department of Statistics, University of Florida, Gainesville, USA
c Department of Mathematics, Faculty of Science, Ankara University, Tandogan, Ankara, Turkey
d Department of Mathematics and Statistics, University of Regina, Saskatchewan, Canada
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DOI: https://doi.org/10.4213/tvp5398
Abstract: Uniform integrability is an interesting concept in probability theory and functional analysis since it plays an important role in establishing laws of large numbers. In the literature, there are several versions of uniform integrability. Some are defined with the help of matrix summability methods, such as the Cesàro matrix, or more general methods. In this paper, we introduce a new version of uniform integrability via power series summability methods. We investigate the relationships of this new concept with some previous concepts and give $L_1$- and $L_2$-convergence results for the laws of large numbers.
Keywords: uniform integrability, power series summability method, $L_1$-convergence.
Funding agency Grant number
Consejería Economía, Innovación, Ciencia y Empleo, Junta de Andalucía P08-FQM-03543
Ministerio de Educación y Ciencia, Spain MTM2015-65242-C2-1-P
Scientific and Technological Research Council of Turkey (TÜBITAK) 1059B191800534
Kazan' Federal University 1.13556.2019/13.1
The research of M. Ordóñez Cabrera has been partially supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 grant P08-FQM-03543, and by MEC grant MTM2015-65242-C2-1-P. The research of M. Ünver was done while he was visiting University of Regina, Canada and has been supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) grant 1059B191800534. The research of A. Volodin has been partially supported by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project 1.13556.2019/13.1.
Received: 26.02.2020
Revised: 13.01.2021
Accepted: 13.01.2021
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 1, Pages 89–104
DOI: https://doi.org/10.1137/S0040585X97T990770
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Ordóñez Cabrera, A. Rosalsky, M. Ünver, A. Volodin, “A new version of uniform integrability via power series summability methods”, Teor. Veroyatnost. i Primenen., 67:1 (2022), 115–133; Theory Probab. Appl., 67:1 (2022), 89–104
Citation in format AMSBIB
\Bibitem{OrdRosUnv22}
\by M.~Ord\'o\~nez Cabrera, A.~Rosalsky, M.~\"Unver, A.~Volodin
\paper A new version of uniform integrability via power series summability methods
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 1
\pages 115--133
\mathnet{http://mi.mathnet.ru/tvp5398}
\crossref{https://doi.org/10.4213/tvp5398}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4466415}
\zmath{https://zbmath.org/?q=an:1489.60040}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 1
\pages 89--104
\crossref{https://doi.org/10.1137/S0040585X97T990770}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85131092996}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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