Modified Stieltjes Transform and Generalized Convolutions of Probability Distributions

Modified Stieltjes Transform and Generalized Convolutions of Probability Distributions

The classical Stieltjes transform is modified in such a way as to generalize both Stieltjes and Fourier transforms. This transform allows the introduction of new classes of commutative and non-commutative generalized convolutions. A particular case of such a convolution for degenerate distributions...

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Bibliographic Details
Main Authors: Lev B. Klebanov, Rasool Roozegar
Format: Article
Language:English
Published: MDPI AG 2018-01-01
Series:Journal of Risk and Financial Management
Subjects:
Stieltjes transform
characteristic function
generalized convolution
beta distribution
Online Access:http://www.mdpi.com/1911-8074/11/1/5
Description
Summary:The classical Stieltjes transform is modified in such a way as to generalize both Stieltjes and Fourier transforms. This transform allows the introduction of new classes of commutative and non-commutative generalized convolutions. A particular case of such a convolution for degenerate distributions appears to be the Wigner semicircle distribution.
ISSN:1911-8074

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