Infinite divisibility of α-Cauchy distributions
Abstract
In 2009, Yano, Yano and Yor proposed the question of studying the infinite divisibility of the α-Cauchy variable Cα for α>1. The particular case C2 is the well-known standard Cauchy variable, which is infinitely divisible and indeed stable. For α≠2, the infinite divisibility of Cα is previously unknown. In this paper, we prove that Cα is infinitely divisible if and only if 1
Fields of Study & Subjects
Random Matrices and Applications
Probability and Risk Models
Approximation Theory and Sequence Spaces
Publication details
- Journal / source
- Electronic Communications in Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–8
- Publication date
- 1 January 2026