REGULAR VARIATION FOR MEASURES ON METRIC SPACES

被引：95

作者：

Hult, Henrik ^{[1
]}

Lindskog, Filip ^{[2
]}

机构：

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[2] KTH, Dept Math, Stockholm, Sweden

来源：

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2006年 / 80卷 / 94期

关键词：

D O I：

10.2298/PIM0694121H

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The foundations of regular variation for Borel measures on a complete 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. Regular 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 R-d 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.

引用

页码：121 / 140

页数：20

共 23 条

[11] MAX-INFINITELY DIVISIBLE AND MAX-STABLE SAMPLE CONTINUOUS-PROCESSES [J].