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

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 the maximum of observed random variables from the set {X1,...,Xn}. We determine the limiting distribution of random vector 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.