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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
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.
Received: 11.01.2022 Revised: 02.02.2022 Accepted: 07.02.2022
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
Linking options:
https://www.mathnet.ru/eng/tvp5554https://doi.org/10.4213/tvp5554 https://www.mathnet.ru/eng/tvp/v67/i4/p627
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Abstract page: | 161 | Full-text PDF : | 21 | References: | 47 | First page: | 9 |
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