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SECOND ORDER SUBEXPONENTIALITY AND INFINITE DIVISIBILITY
- Source :
- Journal of the Australian Mathematical Society. 112:367-390
- Publication Year :
- 2020
- Publisher :
- Cambridge University Press (CUP), 2020.
-
Abstract
- 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.
- Subjects :
- Distribution (number theory)
General Mathematics
010102 general mathematics
Mathematical analysis
Order (ring theory)
Convolution power
01 natural sciences
Measure (mathematics)
Exponential function
Moment (mathematics)
010104 statistics & probability
0101 mathematics
Real line
Infinite divisibility
Mathematics
Subjects
Details
- ISSN :
- 14468107 and 14467887
- Volume :
- 112
- Database :
- OpenAIRE
- Journal :
- Journal of the Australian Mathematical Society
- Accession number :
- edsair.doi...........20fac09895d84878f7ff7d6782f46fbf