Electronic Journal of Probability
- Electron. J. Probab.
- Volume 23 (2018), paper no. 101, 36 pp.
Limit theorems for free Lévy processes
We consider different limit theorems for additive and multiplicative free Lévy processes. The main results are concerned with positive and unitary multiplicative free Lévy processes at small times, showing convergence to log free stable laws for many examples. The additive case is much easier, and we establish the convergence at small or large times to free stable laws. During the investigation we found out that a log free stable law with index $1$ coincides with the Dykema-Haagerup distribution. We also consider limit theorems for positive multiplicative Boolean Lévy processes at small times, obtaining log Boolean stable laws in the limit.
Electron. J. Probab., Volume 23 (2018), paper no. 101, 36 pp.
Received: 29 November 2017
Accepted: 14 September 2018
First available in Project Euclid: 4 October 2018
Permanent link to this document
Digital Object Identifier
Primary: 46L54: Free probability and free operator algebras
Secondary: 46L53: Noncommutative probability and statistics 60E07: Infinitely divisible distributions; stable distributions 60F05: Central limit and other weak theorems
Arizmendi, Octavio; Hasebe, Takahiro. Limit theorems for free Lévy processes. Electron. J. Probab. 23 (2018), paper no. 101, 36 pp. doi:10.1214/18-EJP224. https://projecteuclid.org/euclid.ejp/1538618571