Regular variation and stability of random measures

Nam Bui Quang; Phuc Ho Dang

doi:10.4134/JKMS.j160361

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2017; 54(3): 1049-1061

Online first article February 16, 2017 Printed May 1, 2017

https://doi.org/10.4134/JKMS.j160361

Regular variation and stability of random measures

Nam Bui Quang and Phuc Ho Dang

Academy of Air Defence and Air Forces, Vietnam Academy of Sciences and Technology

Abstract

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Abstract

The paper presents a characterization of stable random measures, giving a canonical form of their Laplace transform. Domain of attraction of stable random measures is concerned in a theorem showing that a random measure belongs to domain of attraction of any stable random measures if and only if it varies regularly at infinity.

Keywords: random measure, stable, domain of attraction, regular variation

MSC numbers: Primary 60E07; Secondary 60B12