**10. Conclusions**

In this paper, multivariate probability distributions were considered that are representable as scale mixtures of multivariate stable distributions. Multivariate analogs of the Mittag–Leffler distribution were introduced. Some properties of these distributions were discussed. Attention was paid to the representations of the corresponding random vectors as products of independent random variables and vectors. In these products, relations were traced of the distributions of the involved terms with popular probability distributions. As examples of distributions of the class of scale mixtures of multivariate stable distributions, multivariate generalized Linnik distributions and multivariate generalized Mittag–Leffler distributions were considered in detail. Their relations with multivariate 'ordinary' Linnik distributions, multivariate normal, stable and Laplace laws as well as with univariate Mittag–Leffler and generalized Mittag–Leffler distributions were discussed. Limit theorems were proved presenting necessary and sufficient conditions for the convergence of the distributions of random sequences with independent random indices (including sums of a random number of random vectors and multivariate statistics constructed from samples with random sizes) to scale mixtures of multivariate elliptically contoured stable distributions. The property of scale-mixed multivariate elliptically contoured stable distributions to be both scale mixtures of a non-trivial multivariate stable distribution and a normal scale mixture was used to obtain necessary and sufficient conditions for the convergence of the distributions of random sums of random vectors with covariance matrices to the multivariate generalized Linnik distribution.

The key points of the paper are:


**Author Contributions:** Conceptualization, Y.K., V.K. and A.Z.; methodology, Y.K. and V.K.; validation, Y.K. and V.K.; investigation, Y.K., V.K. and A.Z.; supervision, V.K.; project administration, V.K. and A.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by Russian Science Foundation, project 18-11-00155.

**Conflicts of Interest:** The authors declare no conflict of interest.
