STABLE RANDOM VARIABLES WITH COMPLEX STABILITY INDEX, II

被引：0
|
作者：
Alexeev, I. A. [1 ,2 ]
机构：
[1] Russian Acad Sci, St Petersburg Dept, Steklov Math Inst, St Petersburg 191023, Russia
[2] Russian Acad Sci, Kharkeich Inst, Inst Informat Transmiss Problems, Moscow, Russia
来源：
THEORY OF PROBABILITY AND ITS APPLICATIONS | 2022年 / 67卷 / 04期
基金：
俄罗斯科学基金会;
关键词：
infinitely divisible distributions; operator-stable laws; limit theorems; stable distributions;
D O I：
暂无
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
This paper, which isa 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 Levy 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.
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页码：499 / 515
页数：17
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