Modified Stieltjes Transform and Generalized Convolutions of Probability Distributions

Journal of Risk and Financial Management

Lev B. Klebanov¹  Rasool Roozegar² 

[1] Department of Probability and Mathematical Statistics, MFF, Charles University, Prague 1, 116 36, Czech Republic;Department of Statistics, Yazd University, Yazd 89195-741, Iran;

关键词: Stieltjes transform;    characteristic function;    generalized convolution;    beta distribution;   

DOI  :  10.3390/jrfm11010005

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown