V_a - 变形自由卷积和方差函数

Pub Date : 2024-01-31 DOI:10.1515/gmj-2024-2004

Raouf Fakhfakh

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引用次数: 0

摘要

本文将讨论 V a {V_{a}} 变形自由卷积的概念。 -变形自由卷积的概念。D. Krystek 和 L. J. Wojakowski, Associative convolutions arising from conditionally free convolution, Infin.Dimens.Anal.Quantum Probab.Relat.Top.8 2005, 3, 515-545], 从与 Cauchy-Stieltjes 核（CSK）族及其相应方差函数理论相关的角度出发。我们确定了 V a {V_{a}} 的幂下的方差函数公式。 -变形自由卷积下的方差函数公式。然后，我们提供了由 V a {V_{a}} 变形自由泊松分布生成的 CSK 族元素的近似值。 -变形自由泊松分布产生的 CSK 族元素的近似值。

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V_a -deformed free convolution and variance function

In this paper, we deal with the notion of V a

{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

{V_{a}}

-deformed free convolution. Then we provide an approximation of elements of the CSK family generated by V a

{V_{a}}

-deformed free Poisson distribution.

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