THE WIENER CONDITION AND THE CONJECTURES OF EMBRECHTS AND GOLDIE

THE WIENER CONDITION AND THE CONJECTURES OF EMBRECHTS AND GOLDIE

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...

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Veröffentlicht in:The Annals of probability 2019-05, Vol.47 (3), p.1221-1239
1. Verfasser: Watanabe, Toshiro
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0091-1798
2168-894X
DOI:10.1214/17-AOP1195