Ergodic behaviour of extreme values

Abstract

AbstractLet {Xn, n ≥ 1} be independent identically distributed random variables with a common non-degenerate distribution function F. For each n ≥ 1, denote Mn = max {X1,…, Xn}. Under certain conditions on F, there exist constants an > 0 and bn ∈ R such that . In this paper, we shall show that {(Mn – bn)/an} exhibits ergodic behaviour under additional conditions of F.