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

Let ( X n ) be a strictly stationary random sequence and M n = max { X 1 , … , X n } . Suppose that some of the random variables X 1 , X 2 , … can be observed and denote by M ˜ n the maximum of observed random variables from the set { X 1 , … , X n } . We determine the limiting distribution of random vector ( M ˜ n , M n ) 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.