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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:116

Article

Mladenovic, Pavle ; Piterbarg, Vladimir

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

DOI  :  10.1016/j.spa.2006.05.009

来源: Elsevier

【 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.

【 授权许可】

Free