The conjectures of Embrechts and Goldie

Abstract

It is shown that the class of convolution equivalent distributions and the class of locally subexponential distributions are not closed under convolution roots. Moreover, two sufficient conditions for the closure under convolution roots of the class of convolution equivalent distributions are given.

15 pages

Cited by in corpus (2)

• On closedness under convolution roots related to an infinitely divisible distribution in the distribution class L(γ)
• Some positive conclusions related to the Embrechts-Goldie' conjecture