Cauchy-Stieltjes kernels families and free multiplicative convolution
Probability
2020-04-16 v1
Abstract
In this paper, we determine the effect of the free multiplicative convolution on the pseudo-variance function of a Cauchy-Stieltjes kernel family. We then use the machinery of variance functions to establish some limit theorems related to this type of convolution and involving the free additive convolution and the boolean additive convolution.
Cite
@article{arxiv.2004.07191,
title = {Cauchy-Stieltjes kernels families and free multiplicative convolution},
author = {Abdelhamid Hassairi and Raouf Fakhfakh},
journal= {arXiv preprint arXiv:2004.07191},
year = {2020}
}
Comments
We determine the effect of the free multiplicative convolution on the pseudo-variance function of a Cauchy-Stieltjes kernel family