ИСТИНА

Random sums are used very often in applied investigations. In one-dimensional case is very popular the model of random sum with index which has geometric distribution. If the summands are independent and identically distributed the limit distribution will be geometric-stable (see the paper by Klebanov 1984). The most popular example are Mittag-Leffler and Linnik distributions. In two paper by Korolev (2016, 2017) the properties of these distributions and their relations with other distributions were investigated in many details. We consider the multivariate generalization of this problem. This problem is not new, but in papers of other authors it is considered the case of multivariate random sums with common index for all components of the sum. We consider the more general case where the multivariate index of the sum has multivariate geometric distribution with dependent components. We define the notion of multivariate geometric-stable distributions, consider the multivariate analogs of Mittag-Leffler and Linnik distributions, investigate their properties and relations with other distributions using scale mixtures and subordinated processes. This research is supported by RSCF, project 18-11-00155