On a Multivariate Analog of the Zolotarev Problem

A generalized multivariate problem due to V. M. Zolotarev is considered. Some related results on geometric random sums and (multivariate) stable distributions are extended a more general case of “anisotropic” summation where independent vectors with index having special distribution Anisotropic-geometric introduced. It demonstrated that these coordinate-wise scale mixtures elliptically contoured the Marshall–Olkin mixing distributions. The corresponding analogs Laplace, Linnik Mittag–Leffler relations between presented.