Abstract
We show that a Cramér–Wold device holds for infinite divisibility of Zd-valued distributions, i.e. that the distribution of a Zd-valued random vector X is infinitely divisible if and only if the distribution of aTX is infinitely divisible for all a∈Rd, and that this in turn is equivalent to infinite divisibility of the distribution of aTX for all a∈N0d. A key tool for proving this is a Lévy–Khintchine type representation with a signed Lévy measure for the characteristic function of a Zd-valued distribution, provided the characteristic function is zero-free.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
