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Remarks on the relation between fractional moments and fractional derivatives of characteristic functions

Published online by Cambridge University Press:  14 July 2016

G. Laue
G. Laue*
Affiliation:
Karl-Marx-Universität, Leipzig
*
∗Postal address: Karl-Marx-Universität, Sektion Mathematik, 701 Leipzig, Karl-Marx-Platz, DDR-German Democratic Republic.
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Abstract

We consider fractional derivatives of characteristic functions. We use these fractional derivatives for the formulation of new conditions for the existence of non-integer moments. We also compare the known conditions for the existence of moments of arbitrary random variables with our new conditions. As a consequence many conditions can be written in a unified terminology.

Keywords

CHARACTERISTIC FUNCTIONSMOMENTSFRACTIONAL DERIVATIVES
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 456 - 466
Copyright
Copyright © Applied Probability Trust 1980 

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References

[1] Bronstein, I. N. and Semendjajew, K. A. (1967) Taschenbuch der Mathematik. Leipzig.Google Scholar
[2] Brown, B. M. (1970) Characteristic functions, moments and the central limit theorem. Ann. Math. Statist. 41, 658–664.Google Scholar
[3] Girlich, H.-J. and Rossberg, H.-J. (1971) Eine neue Methode zum Studium des Zusammenhanges zwischen charakteristischen Funktionen und Momenten sowie Semi-Invarianten. Math. Nachr. 51, 123–147.CrossRefGoogle Scholar
[4] Kawata, T. (1970) Fourier Series in Probability Theory. Academic Press, New York.Google Scholar
[5] Laue, G. (1973) Zur Theorie der charakteristischen Funktionen nichtnegativer Zufallsgrössen. Trans. 6th Prague Conf., 529–546.Google Scholar
[6] Marchaud, A. (1927) Sur les derivées et sur les différences des fonctions de variables réelles. J. Math. Pures Appl. 6, 337–425.Google Scholar
[7] Ramachandran, R. (1969) On characteristic functions and moments. Sankya A 31, 1–12.Google Scholar
[8] Wolfe, S. J. (1973) On the local behavior of characteristic functions. Ann. Prob. 1, 862–866.Google Scholar
[9] Wolfe, S. J. (1975) On moments of probability distribution functions. In Lecture Notes in Mathematics 457, Springer-Verlag, Berlin, 306–316.Google Scholar