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Modified Stieltjes Transform and Generalized Convolutions of Probability Distributions

Author

Listed:
  • Lev B. Klebanov

    (Department of Probability and Mathematical Statistics, MFF, Charles University, Prague 1, 116 36, Czech Republic)

  • Rasool Roozegar

    (Department of Statistics, Yazd University, Yazd 89195-741, Iran)

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.

Suggested Citation

  • Lev B. Klebanov & Rasool Roozegar, 2018. "Modified Stieltjes Transform and Generalized Convolutions of Probability Distributions," JRFM, MDPI, vol. 11(1), pages 1-6, January.
    • Handle: RePEc:gam:jjrfmx:v:11:y:2018:i:1:p:5-:d:126902
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    Cited by:

    1. Stephen Chan & Saralees Nadarajah, 2020. "Extreme Values and Financial Risk," JRFM, MDPI, vol. 13(2), pages 1-3, February.

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