Operator-stable laws

William N. Hudson and J. David Mason

Journal of Multivariate Analysis, 1981, vol. 11, issue 3, 434-447

Abstract: Sharpe investigated the structure of full operator-stable measures [mu] on a vector group V and obtained decompositions, [mu] = [mu]1 * [mu]2 and V = V1 [circle plus operator] V2, in terms of the Gaussian component [mu]1 and the Poisson component [mu]2. The subspaces V1 and V2 are here identified in terms of an exponent B for [mu]. Sharpe also pointed out that the Lévy measure M of [mu] is a mixture of Lévy measures concentrated on single orbits of tB. Here, an explicit representation is obtained for M as such a mixture by constructing a measure on the unit sphere. Also, necessary and sufficient conditions are given that a Lévy measure be the Lévy measure of a full operator-stable measure. The final result deals with full Gaussian measures [mu] and establishes the connection between its covariance operator and the class of all exponents of [mu].

Keywords: Operator-stable; distributions; multivariate; stable; laws; central; limit; theorem (search for similar items in EconPapers)
Date: 1981
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(81)90086-5
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:11:y:1981:i:3:p:434-447

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 ().