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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 4, Pages 627–648
DOI: https://doi.org/10.4213/tvp5554 (Mi tvp5554) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Stable random variables with complex stability index, II

I. A. Alekseevab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
Full-text PDF (474 kB) Citations (2)
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DOI: https://doi.org/10.4213/tvp5554
Abstract: This paper, which is a continuation of [I. A. Alexeev, Theory Probab. Appl., 67 (2022), pp. 335–351], is concerned with $\alpha$-stable distributions with complex stability index $\alpha$. Sufficient conditions for membership in the domain of attraction of $\alpha$-stable random variables (r.v.'s) are given, and $\alpha$-stable Lévy processes and the corresponding semigroups of operators are constructed. Necessary and sufficient conditions are given for membership in the class of limit laws for sums of independent and identically distributed (i.i.d.) complex r.v.'s with complex normalization and centering.
Keywords: infinitely divisible distributions, operator-stable laws, limit theorems, stable distributions.
Funding agency Grant number
Russian Science Foundation 22-21-00016
This research was carried out with the financial support of the Russian Science Foundation (grant 22-21-00016).
Received: 11.01.2022
Revised: 02.02.2022
Accepted: 07.02.2022
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 4, Pages 499–515
DOI: https://doi.org/10.1137/S0040585X97T991118
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. A. Alekseev, “Stable random variables with complex stability index, II”, Teor. Veroyatnost. i Primenen., 67:4 (2022), 627–648; Theory Probab. Appl., 67:4 (2022), 499–515
Citation in format AMSBIB
\Bibitem{Ale22}
\by I.~A.~Alekseev
\paper Stable random variables with complex stability index, II
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 4
\pages 627--648
\mathnet{http://mi.mathnet.ru/tvp5554}
\crossref{https://doi.org/10.4213/tvp5554}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 4
\pages 499--515
\crossref{https://doi.org/10.1137/S0040585X97T991118}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85153279423}
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  • https://doi.org/10.4213/tvp5554
  • https://www.mathnet.ru/eng/tvp/v67/i4/p627
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