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

1 June 1980

journal article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 17 (2) , 456-466
https://doi.org/10.2307/3213035

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

This publication has 3 references indexed in Scilit:

On the Local Behavior of Characteristic Functions
The Annals of Probability, 1973
Eine neue Methode zum Studium des Zusammenhanges zwischen charakteristischen Funktionen und Momenten sowie Semi‐Invarianten
Mathematische Nachrichten, 1971
Characteristic Functions, Moments, and the Central Limit Theorem
The Annals of Mathematical Statistics, 1970