Operator-stable distributions and stable marginals

William N. Hudson

Journal of Multivariate Analysis, 1980, vol. 10, issue 1, 26-37

Abstract: Sharpe has shown that full operator-stable distributions [mu] on Rn are infinitely divisible and for a suitable automorphism B depending on [mu] satisfy the relation [mu]t = [mu]t-B * [delta](b(t)) for all t > 0. B is called an exponent for [mu]. It is proved here that if an operator-stable distribution on Rn has n linearly independent univariate stable marginals, then its exponents are semi-simple operators. In addition necessary and sufficient conditions are given for such a distribution on R2 to have univariate stable marginals. The proofs use a hitherto unpublished result of Sharpe's that all full operator-stable distributions are absolutely continuous. His proof is provided here.

Date: 1980
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(80)90079-2
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:10:y:1980:i:1:p:26-37

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().