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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, Volume 7, Issue 3, Pages 418–424
DOI: https://doi.org/10.21638/spbu01.2020.305 (Mi vspua166) 		 
This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

On the strong law of large numbers for linear combinations of concomitants

O. I. Dudkinaa, N. V. Gribkovaab

a St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
b St. Petersburg State Transport University, 9, Moskovskiy pr., St. Petersburg, 190031, Russian Federation
Full-text PDF (288 kB) Citations (3)
DOI: https://doi.org/10.21638/spbu01.2020.305
Abstract: The article proves a theorem on the strong law of large numbers for linear functions of concomitants (induced order statistics) for sequences of independent identically distributed two-dimensional random vectors. The result complements previous work by Yang (1981), Gribkova and Zitikis (2017, 2019). The proof is based on the conditional independence property of concomitants Bhattacharya (1974), the strong law of large numbers for functions of order statistics by van Zwet (1980) is used, classical inequalities apply, including Rosenthal's (1970).
Keywords: concomitants, induced order statistics, linear combinations, strong law of large numbers.
Received: 22.12.2019
Revised: 20.01.2020
Accepted: 19.03.2020
English version:
Vestnik St. Petersburg University, Mathematics, 2020, Volume 7, Issue 3, Pages 282–286
DOI: https://doi.org/10.1134/S1063454120030061
Document Type: Article
UDC: 519.2
MSC: 60F15, 62G30, 62G20; 60F05, 62G05
Language: Russian
Citation: O. I. Dudkina, N. V. Gribkova, “On the strong law of large numbers for linear combinations of concomitants”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:3 (2020), 418–424; Vestn. St. Petersbg. Univ., Math., 7:3 (2020), 282–286
Citation in format AMSBIB
\Bibitem{DudGri20}
\by O.~I.~Dudkina, N.~V.~Gribkova
\paper On the strong law of large numbers for linear combinations of concomitants
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2020
\vol 7
\issue 3
\pages 418--424
\mathnet{http://mi.mathnet.ru/vspua166}
\crossref{https://doi.org/10.21638/spbu01.2020.305}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2020
\vol 7
\issue 3
\pages 282--286
\crossref{https://doi.org/10.1134/S1063454120030061}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
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