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 ones are given. Some variants of the Linnik and Polya theorems are given.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 466, 2017, pp. 81–95.
Translated by S. Yu. Pilyugin.
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Volchenkova, I.V., Klebanov, L.B. On Characterization of Distributions of Symmetrically Dependent Random Variables. J Math Sci 244, 752–761 (2020). https://doi.org/10.1007/s10958-020-04648-w