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

[31] Multi-modal tempered stable distributions and prosses with applications to finance
Arefi, Ahmad
Pourtaheri, Reza
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2020, 49 (17) : 4133 - 4149
[32] STABLE EQUIVALENCE OF THE WEAK CLOSURES OF FREE GROUPS CONVOLUTION-ALGEBRAS
RADULESCU, F
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1993, 156 (01) : 17 - 36
[33] ON ASYMPTOTIC EXPANSIONS FOR CONVOLUTION OF DISTRIBUTIONS WHICH BELONG TO STABLE LAWS
Syulyukin, A. V.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2014, 58 (03) : 518 - 524
[34] Weighted convolution algebras on subsemigroups of the real line
Dales, H. G.
Dedania, H. V.
DISSERTATIONES MATHEMATICAE, 2009, (459) : 5 - +
[35] Dual Convolution for the Affine Group of the Real Line
Choi, Yemon
Ghandehari, Mahya
COMPLEX ANALYSIS AND OPERATOR THEORY, 2021, 15 (04)
[36] Dual Convolution for the Affine Group of the Real Line
Yemon Choi
Mahya Ghandehari
Complex Analysis and Operator Theory, 2021, 15
[37] Random integral representations for free-infinitely divisible and tempered stable distributions
Jurek, Zbigniew J.
STATISTICS & PROBABILITY LETTERS, 2007, 77 (04) : 417 - 425
[38] On the support of tempered distributions
Vieli, F. J. Gonzalez
Graham, Colin C.
ARCHIV DER MATHEMATIK, 2007, 88 (02) : 133 - 142
[39] Polynomial tempered distributions
Sharyn, S., V
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2010, 2 (02) : 123 - 132
[40] On the support of tempered distributions
F. J. González Vieli
Colin C. Graham
Archiv der Mathematik, 2007, 88 : 133 - 142

← 1 2 3 4 5 →