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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 501, Pages 5–10
DOI: https://doi.org/10.31857/S2686954321060023 (Mi danma213) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On stable random variables with a complex stability index

I. A. Alekseev

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
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DOI: https://doi.org/10.31857/S2686954321060023
Abstract: In this paper, we construct complex-valued random variables that satisfy the usual stability condition, but for a complex stability index $\alpha$ satisfying the conditions $|\alpha-1|<1$ and $|\alpha-\frac12|\ne\frac12$. A representation of the characteristic functions of the constructed random variables is found, and limit theorems for sums of independent identically distributed random variables are formulated.
Keywords: stable distributions, infinitely divisible distributions, limit theorems.
Presented: I. A. Ibragimov
Received: 31.08.2021
Revised: 18.09.2021
Accepted: 22.09.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 3, Pages 317–321
DOI: https://doi.org/10.1134/S1064562421060028
Bibliographic databases:
Document Type: Article
UDC: 519.213.7
Language: Russian
Citation: I. A. Alekseev, “On stable random variables with a complex stability index”, Dokl. RAN. Math. Inf. Proc. Upr., 501 (2021), 5–10; Dokl. Math., 104:3 (2021), 317–321
Citation in format AMSBIB
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