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February, 1975 Equivalence of Infinitely Divisible Distributions
William N. Hudson, Howard G. Tucker
Ann. Probab. 3(1): 70-79 (February, 1975). DOI: 10.1214/aop/1176996449

Abstract

If $F$ is an infinitely divisible distribution function without a Gaussian component whose Levy spectral measure $M$ is absolutely continuous and $M(\mathbb{R}^1\backslash\{0\}) = \infty$, then $F$ is shown to have an a.e. positive density over its support; this support of $F$ is always an interval of the form $(-\infty, \infty), (-\infty, a\rbrack$ or $\lbrack a, \infty)$. In addition, sufficient conditions are obtained for two infinitely divisible distribution functions without Gaussian components to be absolutely continuous with respect to each other, i.e., equivalent.

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William N. Hudson. Howard G. Tucker. "Equivalence of Infinitely Divisible Distributions." Ann. Probab. 3 (1) 70 - 79, February, 1975. https://doi.org/10.1214/aop/1176996449

Information

Published: February, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0303.60011
MathSciNet: MR372944
Digital Object Identifier: 10.1214/aop/1176996449

Subjects:
Primary: 60E05

Keywords: absolute continuity of measures , equivalence of measures , Infitely divisible distribution functions and characteristic functions

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 1 • February, 1975
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