## The Annals of Probability

### Infinitely Divisible Distributions with Unimodal Levy Spectral Functions

Thomas A. O'Connor

#### Abstract

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.

#### Article information

Source
Ann. Probab. Volume 7, Number 3 (1979), 494-499.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995049

Digital Object Identifier
doi:10.1214/aop/1176995049

Mathematical Reviews number (MathSciNet)
MR528326

Zentralblatt MATH identifier
0401.60015

JSTOR