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The Wiener condition and the conjectures of Embrechts and Goldie
- Source :
- Ann. Probab. 47, no. 3 (2019), 1221-1239
- Publication Year :
- 2019
- Publisher :
- The Institute of Mathematical Statistics, 2019.
-
Abstract
- We show that the class of convolution equivalent distributions and the class of locally subexponential distributions are not closed under convolution roots. It gives a negative answer to the classical conjectures of Embrechts and Goldie. Moreover, we establish two sufficient conditions in order that the class of convolution equivalent distributions is closed under convolution roots.
- Subjects :
- Statistics and Probability
62E20
Class (set theory)
Pure mathematics
60G50
010102 general mathematics
convolution roots
local subexponentiality
01 natural sciences
Convolution
Negative - answer
010104 statistics & probability
Convolution equivalence
Wiener condition
Order (group theory)
60E05
0101 mathematics
Statistics, Probability and Uncertainty
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Ann. Probab. 47, no. 3 (2019), 1221-1239
- Accession number :
- edsair.doi.dedup.....fe67165422405a344955c2e78a21e94a