The Development of the Mathematical Theory of Extremes in the Past Half Century

Abstract

This paper is a survey of development of extreme value theory during the last half century from a mathematician’s point of view. The paper considers both general results for classical models (schemes of maximum of independent identically distributed random variables under linear normalization) and extentions of the classical models and the derivations from the classical assumptions also. Different approaches to the characterization theorems for limiting distributions are discribed. The results on the estimation of the rate of convergence in limiting theorems and random sample sizes are given. The paper gives a survey of different approaches to the extreme value theory based on other problems of probability theory.