Translator Disclaimer
May 2019 The Wiener condition and the conjectures of Embrechts and Goldie
Toshiro Watanabe
Ann. Probab. 47(3): 1221-1239 (May 2019). DOI: 10.1214/17-AOP1195

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.

Citation

Download Citation

Toshiro Watanabe. "The Wiener condition and the conjectures of Embrechts and Goldie." Ann. Probab. 47 (3) 1221 - 1239, May 2019. https://doi.org/10.1214/17-AOP1195

Information

Received: 1 February 2016; Revised: 1 April 2017; Published: May 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07067268
MathSciNet: MR3945745
Digital Object Identifier: 10.1214/17-AOP1195

Subjects:
Primary: 60E05, 60G50, 62E20

Rights: Copyright © 2019 Institute of Mathematical Statistics

JOURNAL ARTICLE
19 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 3 • May 2019
Back to Top