Closure under infinitely divisible distribution roots and the Embrechts–Goldie conjecture

We show that the distribution class L(γ) \ OS is not closed under infinitely divisible distribution roots for γ > 0, that is, we provide some infinitely divisible distributions belonging to the class, whereas the corresponding Lévy distributions do not. In fact, one part of these Lévy distributio...

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Veröffentlicht in:Lithuanian mathematical journal 2024, Vol.64 (1), p.101-114
Hauptverfasser: Xu, Hui, Yu, Changjun, Wang, Yuebao, Cheng, Dongya
Format: Artikel
Sprache:eng
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Zusammenfassung:We show that the distribution class L(γ) \ OS is not closed under infinitely divisible distribution roots for γ > 0, that is, we provide some infinitely divisible distributions belonging to the class, whereas the corresponding Lévy distributions do not. In fact, one part of these Lévy distributions belonging to the class OL\L(γ) have different properties, and the other parts even do not belong to the class OL. Therefore, combining with the existing related results, we give a completely negative conclusion for the subject and Embrechts–Goldie conjecture. Then we discuss some interesting issues related to the results of this paper.
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-024-09620-8