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Stability of Maxima of Random Variables with Multidimensional Indices
Authors:Email author" target="_blank">Michael?Z?F?LiEmail author  R?J?Tomkins
Institution:(1) Nanyang Business School, Nanyang Technological University, Nanyang Avenue, Singapore, 639798;(2) Department of Mathematics and Statistics, University of Regina, Regina, SK, S4S 0A2, Canada
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).AMS 2000 Subject Classification. Primary—60F15, 60G60, 62G30, Secondary—10A25, 60G99
Keywords:i  i  d  random variables  maxima  multidimensional indices  stability theorems
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