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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
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.
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
Linking options:
https://www.mathnet.ru/eng/danma213 https://www.mathnet.ru/eng/danma/v501/p5
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