Stability of Maxima of Random Variables with Multidimensional Indices

摘要

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).