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J. Risk Financial Manag. 2018, 11(1), 5; https://doi.org/10.3390/jrfm11010005

Modified Stieltjes Transform and Generalized Convolutions of Probability Distributions

1
Department of Probability and Mathematical Statistics, MFF, Charles University, Prague 1, 116 36, Czech Republic
2
Department of Statistics, Yazd University, Yazd 89195-741, Iran
*
Author to whom correspondence should be addressed.
Received: 3 November 2017 / Revised: 25 December 2017 / Accepted: 11 January 2018 / Published: 14 January 2018
(This article belongs to the Special Issue Extreme Values and Financial Risk)
Full-Text   |   PDF [231 KB, uploaded 14 January 2018]

Abstract

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. View Full-Text
Keywords: Stieltjes transform; characteristic function; generalized convolution; beta distribution Stieltjes transform; characteristic function; generalized convolution; beta distribution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Klebanov, L.B.; Roozegar, R. Modified Stieltjes Transform and Generalized Convolutions of Probability Distributions. J. Risk Financial Manag. 2018, 11, 5.

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