On the convolution equivalence of tempered stable distributions on the real line

被引：0

作者：

Torricelli, Lorenzo ^{[1
]}

机构：

[1] Univ Bologna, Dept Stat Sci P Fortunati, Via Belle Arti 41, I-40126 Bologna, Italy

来源：

STATISTICS & PROBABILITY LETTERS | 2024年 / 207卷

关键词：

Tempered stable distributions; Convolution equivalence; Subexponentiality; Long tails; Heavy tails; CONVERGENCE;

D O I：

10.1016/j.spl.2024.110034

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：

We show the convolution equivalence property of univariate tempered stable distributions in the sense of Rosinski (2007). This makes rigorous various classic heuristic arguments on the asymptotic similarity between the probability and Levy densities of such distributions. Some specific examples from the literature are discussed.

引用

页数：6

共 50 条

[1] Discrete Tempered Stable Distributions
Grabchak, Michael
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2022, 24 (03) : 1877 - 1890
[2] Discrete Tempered Stable Distributions
Michael Grabchak
Methodology and Computing in Applied Probability, 2022, 24 : 1877 - 1890
[3] Tempered stable distributions and processes
Kuechler, Uwe
Tappe, Stefan
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (12) : 4256 - 4293
[4] Solvability of convolution equations in the space of tempered distributions
S. Abdullah
Archiv der Mathematik, 2002, 78 : 481 - 484
[5] CONVOLUTION THEOREMS FOR WAVELET TRANSFORM ON TEMPERED DISTRIBUTIONS AND THEIR EXTENSION TO TEMPERED BOEHMIANS
Roopkumar, R.
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2009, 2 (01) : 117 - 127
[6] Solvability of convolution equations in the space of tempered distributions
Abdullah, S
ARCHIV DER MATHEMATIK, 2002, 78 (06) : 481 - 484
[7] Convolution equivalence and distributions of random sums
Toshiro Watanabe
Probability Theory and Related Fields, 2008, 142 : 367 - 397
[8] Convolution equivalence and distributions of random sums
Watanabe, Toshiro
PROBABILITY THEORY AND RELATED FIELDS, 2008, 142 (3-4) : 367 - 397
[9] ON THE TWISTED CONVOLUTION PRODUCT AND THE WEYL TRANSFORM OF THE TEMPERED DISTRIBUTIONS
MAILLARD, JM
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1984, 298 (02): : 35 - 38
[10] Hankel transformation and Hankel convolution of tempered Beurling distributions
Belhadj, M
Betancor, JJ
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2001, 31 (04) : 1171 - 1203

← 1 2 3 4 5 →