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.
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Acknowledgements
The authors are grateful to two reviewers for their constructive comments and suggestions that have led to significant improvements in the paper.
Funding
The first author research was supported by the Deanship of Scientific Research at Jouf University through research Grant No. (DSR-2021-03-03188).
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Fakhfakh, R., Hassairi, A. Cauchy-Stieltjes Kernel Families and Free Multiplicative Convolution. Commun. Math. Stat. (2023). https://doi.org/10.1007/s40304-022-00311-9
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DOI: https://doi.org/10.1007/s40304-022-00311-9