The Annals of Probability

Equivalence of Infinitely Divisible Distributions

William N. Hudson and Howard G. Tucker

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60E05: Distributions: general theory

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

Citation

Hudson, William N.; Tucker, Howard G. Equivalence of Infinitely Divisible Distributions. Ann. Probab. 3 (1975), no. 1, 70--79. doi:10.1214/aop/1176996449. https://projecteuclid.org/euclid.aop/1176996449


Export citation