A Cramér–Wold device for infinite divisibility of Zd-valued distributions

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

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 aT X is infinitely divisible for all a ∈ Rd, and that this in turn is equivalent to infinite divisibility of the distribution of aT X for all a ∈ Nd0 . A key tool for proving this is a Lévy–Khintchine type representation with a signed Lévy measure for thed.

Details

OriginalspracheEnglisch
Seiten (von - bis)1276-1283
Seitenumfang8
FachzeitschriftBernoulli
Jahrgang28
Ausgabenummer2
PublikationsstatusVeröffentlicht - Mai 2022
Peer-Review-StatusJa

Schlagworte

ASJC Scopus Sachgebiete

Schlagwörter

  • Cramér–Wold device, Infinitely divisible distribution, Quasi-infinitely divisible distribution, Signed Lévy measure

Bibliotheksschlagworte