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Infinitely Divisible Distributions with Unimodal Levy Spectral Functions
Thomas A. O'Connor
The Annals of Probability
Vol. 7, No. 3 (Jun., 1979), pp. 494-499
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2243201
Page Count: 6
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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.
The Annals of Probability © 1979 Institute of Mathematical Statistics