Stability of Maxima of Random Variables with Multidimensional Indices |
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Authors: | Email author" target="_blank">Michael?Z?F?LiEmail author R?J?Tomkins |
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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 |
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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 |
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Keywords: | i i d random variables maxima multidimensional indices stability theorems |
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