2021/07/20 by Hotta, Ikkei, Młotkowski, Wojciech, Sakuma, Noriyoshi +1
#46L54 #60E07 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2107.09473
Inspired by the notion of quasi-infinite divisibility (QID), we introduce and study the class of freely quasi-infinitely divisible (FQID) distributions on ℝ, i.e. distributions which admit the free Lévy-Khintchine-type representation with signed Lévy measure. We prove several properties of the FQID class, some of them in contrast to those of the QID class. For example, a FQID distribution may have negative Gaussian part, and the total mass of its signed Lévy measure may be negative. Finally, we extend the Bercovici-Pata bijection, providing a characteristic triplet, with the Lévy measure having nonzero negative part, which is at the same time classical and free characteristic triplet.