THE WIENER CONDITION AND THE CONJECTURES OF EMBRECHTS AND GOLDIE

• 成果类型: Article
• 署名作者: Watanabe, Toshiro
• 署名单位: University of Aizu
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1195
• 发表日期: 2019
• 页码: 1221-1239
• 关键词: convolution equivalence; infinite-divisibility

摘要

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.