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.
Citation
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
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