SECOND ORDER SUBEXPONENTIALITY AND INFINITE DIVISIBILITY

We characterize the second order subexponentiality of an infinitely divisible distribution on the real line under an exponential moment assumption. We investigate the asymptotic behaviour of the difference between the tails of an infinitely divisible distribution and its Lévy measure. Moreover, we s...

Full description

Saved in:
Bibliographic Details
Published inJournal of the Australian Mathematical Society (2001) Vol. 112; no. 3; pp. 367 - 390
Main Author WATANABE, TOSHIRO
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.06.2022
Subjects
Asymptotic methods
Asymptotic properties
Decomposition
local subexponentiality
infinite divisibility
60E07
second order subexponentiality
60G51
60G50
Online AccessGet full text

Cover

More Information
Summary:We characterize the second order subexponentiality of an infinitely divisible distribution on the real line under an exponential moment assumption. We investigate the asymptotic behaviour of the difference between the tails of an infinitely divisible distribution and its Lévy measure. Moreover, we study the second order asymptotic behaviour of the tail of the $t$ th convolution power of an infinitely divisible distribution. The density version for a self-decomposable distribution on the real line without an exponential moment assumption is also given. Finally, the regularly varying case for a self-decomposable distribution on the half line is discussed.
ISSN:1446-7887
1446-8107
DOI:10.1017/S1446788720000208