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Regular variation for measures on metric spaces
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-9210-121X
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2006 (English)In: Publications de l'Institut Mathématique (Beograd), ISSN 0350-1302, E-ISSN 1820-7405, Vol. 80, no 94, 121-140 p.Article in journal (Refereed) Published
Abstract [en]

The foundations of regular variation for Borel measures on a com- plete separable space S, that is closed under multiplication by nonnegative real numbers, is reviewed. For such measures an appropriate notion of convergence is presented and the basic results such as a Portmanteau theorem, a mapping theorem and a characterization of relative compactness are derived. Regu- lar variation is defined in this general setting and several statements that are equivalent to this definition are presented. This extends the notion of regular variation for Borel measures on the Euclidean space Rd to more general metric spaces. Some examples, including regular variation for Borel measures on Rd, the space of continuous functions C and the Skorohod space D, are provided.

Place, publisher, year, edition, pages
2006. Vol. 80, no 94, 121-140 p.
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-78646DOI: 10.2298/PIM0694121HOAI: oai:DiVA.org:kth-78646DiVA: diva2:492731
Note
QC 20120307Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2017-12-08Bibliographically approved

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Publisher's full texthttp://www.doiserbia.nb.rs/img/doi/0350-1302/2006/0350-13020694121H.pdf

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Hult, Henrik

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