On asymptotic distribution of maxima of complete and incomplete samples from stationary sequences

Abstract

Let (Xn) be a strictly stationary random sequence and Mn = max {X1, ..., Xn}. Suppose that some of the random variables X1, X2, ... can be observed and denote by over(M, ̃)n the maximum of observed random variables from the set {X1, ..., Xn}. We determine the limiting distribution of random vector (over(M, ̃)n, Mn) under some condition of weak dependency which is more restrictive than the Leadbetter condition. An example concerning a storage process in discrete time with fractional Brownian motion as input is also given. © 2006 Elsevier Ltd. All rights reserved.