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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 466, Pages 81–95 (Mi znsl6542)  
On the characterization of distributions of symmetric dependent random variables

I. V. Volchenkova, L. B. Klebanov

Department of Probability and Mathematical Statistics, University, Prague, Czech Republic
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Abstract: Characterizations of scale mixtures of normal, stable and some other laws are obtained in the case of symmetrically dependent random variables. Symmetrically dependent random variables are studied for a special case of scale dependence. Conditions of unique (and nonunique) representation of a sequence of random variables as that of symmetrically dependent are given. Some variants of Linnik and Polya Theorems are given.
Key words and phrases: scale mixtures, normal distribution, stable distributions, characterization of distributions.
Funding agency Grant number
Grantová Agentura České Republiky 16-03708S
Received: 09.10.2017
Document Type: Article
UDC: 519.21
Language: Russian
Citation: I. V. Volchenkova, L. B. Klebanov, “On the characterization of distributions of symmetric dependent random variables”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 81–95
Citation in format AMSBIB
\Bibitem{VolKle17}
\by I.~V.~Volchenkova, L.~B.~Klebanov
\paper On the characterization of distributions of symmetric dependent random variables
\inbook Probability and statistics. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 466
\pages 81--95
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6542}
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