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Extremes

, Volume 7, Issue 2, pp 135–147 | Cite as

Stability of Maxima of Random Variables with Multidimensional Indices

  • Michael Z. F. Li
  • R. J. Tomkins
Original Article
  • 39 Downloads

Abstract

The paper discusses the stability of suitably-defined maxima of a set of i.i.d. random variables with multidimensional indices.It is shown that theorems of Gnedenko (1943) and Tomkins (1986) concerning relative stability and complete relative stability of maxima remain valid in the new setting.Moreover, a criterion for almost sure relative stability for maxima with multidimensional indices is presented, extending a result of Barndorff-Nielsen (1963).

Key words

i.i.d. random variables maxima multidimensional indices stability theorems 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Nanyang Business SchoolNanyang Technological UniversitySingapore
  2. 2.Department of Mathematics and StatisticsUniversity of ReginaReginaCanada

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