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June, 1979 Infinitely Divisible Distributions with Unimodal Levy Spectral Functions
Thomas A. O'Connor
Ann. Probab. 7(3): 494-499 (June, 1979). DOI: 10.1214/aop/1176995049

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.

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Thomas A. O'Connor. "Infinitely Divisible Distributions with Unimodal Levy Spectral Functions." Ann. Probab. 7 (3) 494 - 499, June, 1979. https://doi.org/10.1214/aop/1176995049

Information

Published: June, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0401.60015
MathSciNet: MR528326
Digital Object Identifier: 10.1214/aop/1176995049

Subjects:
Primary: 60E05
Secondary: 60F05

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 3 • June, 1979
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