ИСТИНА

Random sums are very popular in many applied problems. Very often it is assumed that the summation index has a geometric distribution and the summands are independent and identically distributed. We consider a new model in which the summands have distributions belonging to some finite set and are chosen randomly according to some multivariate Bernoulli distribution (see [1]). The limit distributions in such a model have some special form, which we called (by analogy with geometric stable distributions (see [2])) Bernoulli-geometric stable distributions. We introduce a more general definition of the multivariate Linnik distribution and find a connection between this distribution and the multivariate stable, Mittag-Leffler and Weibull distributions. We prove some characterization problem and consider several applications this model in actuarial mathematics and teletraffic theory. This research was carried out in accordance with the scientific program of the Moscow Center for Fundamental and Applied Mathematics and Faculty of Computational Mathematics and Cybernetics in Moscow University.