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

[摘要] Let (X-n) be a strictly stationary random sequence and M, = max{X-1,..., X-n}. Suppose that some of the random variables X-1, X-2,... can be observed and denote by (M) over tilde (n) the maximum of observed random variables from the set {X-1,...,X-n}. We determine the limiting distribution of random vector ((M) over tilde (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. (c) 2006 Elsevier B.V. All rights reserved.

[发布日期] 2006-12-01

[关键词] stationary sequences;weak dependency;missing observations;extreme values;storage process