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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 3, Pages 541–562
DOI: https://doi.org/10.4213/tvp5436 (Mi tvp5436) 		 
Generalized Marcinkiewicz laws for weighted dependent random vectors in Hilbert spaces

T. C. Sona, L. V. Dungb, D. T. Datc, T. T. Trangd

a Vietnam National University, Hanoi University of Science, Hanoi, Vietnam
b The University of Da Nang – University of Science and Education, Da Nang, Vietnam
c Department of Statistics, University of Michigan, Ann Arbor, MI, USA
d Department of Mathematics, University of Alabama, Tuscaloosa, AL, USA
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DOI: https://doi.org/10.4213/tvp5436
Abstract: The aim of this paper is to apply the theory of regularly varying functions for studying Marcinkiewicz weak and strong laws of large numbers for the weighted sum $S_n=\sum_{j=1}^{m_n}c_{nj}X_j$, where $(X_n;\, n\geq 1)$ is a sequence of dependent random vectors in Hilbert spaces, and $(c_{nj})$ is an array of real numbers. Moreover, these results are applied to obtain some results on the convergence of multivariate Pareto–Zipf distributions and multivariate log-gamma distributions.
Keywords: Marcinkiewicz laws of large numbers, dependent random vectors, Hilbert spaces, weighted sums.
Funding agency Grant number
Vietnam National University QG.20.26
This work was supported by the Vietnam National University, Hanoi, under grant QG.20.26.
Received: 10.03.2020
Revised: 22.10.2021
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 3, Pages 434–451
DOI: https://doi.org/10.1137/S0040585X97T991039
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: T. C. Son, L. V. Dung, D. T. Dat, T. T. Trang, “Generalized Marcinkiewicz laws for weighted dependent random vectors in Hilbert spaces”, Teor. Veroyatnost. i Primenen., 67:3 (2022), 541–562; Theory Probab. Appl., 67:3 (2022), 434–451
Citation in format AMSBIB
\Bibitem{SonDunDat22}
\by T.~C.~Son, L.~V.~Dung, D.~T.~Dat, T.~T.~Trang
\paper Generalized Marcinkiewicz laws for weighted dependent random vectors in Hilbert spaces
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 3
\pages 541--562
\mathnet{http://mi.mathnet.ru/tvp5436}
\crossref{https://doi.org/10.4213/tvp5436}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4506222}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 3
\pages 434--451
\crossref{https://doi.org/10.1137/S0040585X97T991039}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85153760209}
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  • https://www.mathnet.ru/eng/tvp/v67/i3/p541
    • Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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