## The Annals of Probability

### Equivalence of Infinitely Divisible Distributions

#### 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.

#### Article information

Source
Ann. Probab., Volume 3, Number 1 (1975), 70-79.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996449

Digital Object Identifier
doi:10.1214/aop/1176996449

Mathematical Reviews number (MathSciNet)
MR372944

Zentralblatt MATH identifier
0303.60011

JSTOR