 On quasi‐infinitely divisible distributions with a point massDavid Berger Mathematische Nachrichten, 2019, vol. 292, issue 8, 1674-1684 Abstract: An infinitely divisible distribution on R is a probability measure μ such that the characteristic function μ̂ has a Lévy–Khintchine representation with characteristic triplet (a,γ,ν), where ν is a Lévy measure, γ∈R and a≥0. A natural extension of such distributions are quasi‐infinitely distributions. Instead of a Lévy measure, we assume that ν is a “signed Lévy measure”, for further information on the definition see [10]. We show that a distribution μ=pδx0+(1−p)μac with p>0 and x0∈R, where μac is the absolutely continuous part, is quasi‐infinitely divisible if and only if μ̂(z)≠0 for every z∈R. We apply this to show that certain variance mixtures of mean zero normal distributions are quasi‐infinitely divisible distributions, and we give an example of a quasi‐infinitely divisible distribution that is not continuous but has infinite quasi‐Lévy measure. Furthermore, it is shown that replacing the signed Lévy measure by a seemingly more general complex Lévy measure does not lead to new distributions. Last but not least it is proven that the class of quasi‐infinitely divisible distributions is not open, but path‐connected in the space of probability measures with the Prokhorov metric. Date: 2019 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:292:y:2019:i:8:p:1674-1684 Ordering information: This journal article can be ordered from Access Statistics for this article Mathematische Nachrichten is currently edited by Robert Denk More articles in Mathematische Nachrichten from Wiley Blackwell |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.