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V_a -deformed free convolution and variance function

  • Raouf Fakhfakh EMAIL logo
Published/Copyright: February 1, 2024
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Abstract

In this paper, we deal with the notion of V a -deformed free convolution, introduced in [A. D. Krystek and L. J. Wojakowski, Associative convolutions arising from conditionally free convolution, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8 2005, 3, 515–545], from a point of view related to the theory of Cauchy–Stieltjes kernel (CSK) families and their corresponding variance functions. We determine the formula for variance function under a power of V a -deformed free convolution. Then we provide an approximation of elements of the CSK family generated by V a -deformed free Poisson distribution.

MSC 2020: 42C10; 46B07

Funding statement: This work was funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No. DGSSR-2023-02-02016.

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Received: 2023-03-24
Revised: 2023-05-17
Accepted: 2023-06-20
Published Online: 2024-02-01
Published in Print: 2024-10-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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