Geodesic
On stable random variables with a complex stability index
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 5-10.

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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. 
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I. A. Alekseev. On stable random variables with a complex stability index. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 5-10. http://geodesic.mathdoc.fr/item/DANMA_2021_501_a0/

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