Regular variation for measures on metric spaces
2006 (English)In: Publications de l'Institut Mathématique (Beograd), ISSN 0350-1302, E-ISSN 0522-828X, Vol. 80, no 94, 121-140 p.Article in journal (Refereed) Published
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.
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-78646DOI: 10.2298/PIM0694121HOAI: oai:DiVA.org:kth-78646DiVA: diva2:492731
QC 201203072012-02-082012-02-082012-03-07Bibliographically approved