On a Multivariate Analog of the Zolotarev Problem

Yury Khokhlov and Victor Korolev
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Yury Khokhlov: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia
Victor Korolev: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia

Mathematics, 2021, vol. 9, issue 15, 1-20

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

Keywords: characterization problems; multivariate geometric random sums; multivariate anisotropic geometric stable distributions; anisotropic multivariate Laplace distribution; anisotropic multivariate Linnik distribution; anisotropic multivariate Mittag–Leffler distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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