Decompositions of multivariate probability distributions

The divisors of multivariate probability distributions are considered that are decreasing at infinity not more slowly than normal distributions and that satisfy various symmetry conditions (in particular, the condition of spherical symmetry).Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei — Trudy Seminara, pp. 72–75, 1980.The author expresses her gratitude to A. A. Zinger with whom she had a discussion during which these problems arose.