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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 454, Pages 151–157 (Mi znsl6389)  
Arak's inequalities for the generalized arithmetic progressions

A. Yu. Zaitsevab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
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Abstract: In 1980's, Arak has obtained powerful inequalities for the concentration functions of sums of independent random variables. Using these results, he has solved an old problem stated by Kolmogorov. In this paper, we will modify one of Arak's results including in the statements the generalized arithmetic progressions.
Key words and phrases: concentration functions, inequalities, sums of independent random variables.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00367
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Received: 30.11.2016
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 229, Issue 6, Pages 698–701
DOI: https://doi.org/10.1007/s10958-018-3708-1
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: A. Yu. Zaitsev, “Arak's inequalities for the generalized arithmetic progressions”, Probability and statistics. Part 24, Zap. Nauchn. Sem. POMI, 454, POMI, St. Petersburg, 2016, 151–157; J. Math. Sci. (N. Y.), 229:6 (2018), 698–701
Citation in format AMSBIB
\Bibitem{Zai16}
\by A.~Yu.~Zaitsev
\paper Arak's inequalities for the generalized arithmetic progressions
\inbook Probability and statistics. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 454
\pages 151--157
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6389}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3602406}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 229
\issue 6
\pages 698--701
\crossref{https://doi.org/10.1007/s10958-018-3708-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042209323}
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