The class of infinitely divisible characteristic functions which have unimodal Levy spectral functions is determined. It is shown that membership in this class is related to solutions of the equations $\phi(u) = \phi^r(ru)\phi_r(u)$, where $r \in (0, 1)$ and $\phi$ and $\phi_r$ are characteristic functions. We point out how elements of this class can serve as limit laws as well as some connections between this class and the class of self-decomposable characteristic functions.
Publié le : 1979-06-14
Classification:
Infinitely divisible characteristic function,
unimodal,
Levy spectral function,
self-decomposable characteristic function,
u.a.n. system of random variables,
central limit theorem,
60E05,
60F05
@article{1176995049,
author = {O'Connor, Thomas A.},
title = {Infinitely Divisible Distributions with Unimodal Levy Spectral Functions},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 494-499},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995049}
}
O'Connor, Thomas A. Infinitely Divisible Distributions with Unimodal Levy Spectral Functions. Ann. Probab., Tome 7 (1979) no. 6, pp. 494-499. http://gdmltest.u-ga.fr/item/1176995049/