The Annals of Applied Probability

Prediction of Stationary Max-Stable Processes

Richard A. Davis and Sidney I. Resnick

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We consider prediction of stationary max-stable processes. The usual metric between max-stable variables can be defined in terms of the $L_1$ distance between spectral functions and in terms of this metric a kind of projection can be defined. It is convenient to project onto max-stable spaces; that is, spaces of extreme value distributed random variables that are closed under scalar multiplication and the taking of finite maxima. Some explicit calculations of max-stable spaces generated by processes of interest are given. The concepts of deterministic and purely nondeterministic stationary max-stable processes are defined and illustrated. Differences between linear and nonlinear prediction are highlighted and some characterizations of max-moving averages and max-permutation processes are given.

Article information

Ann. Appl. Probab., Volume 3, Number 2 (1993), 497-525.

First available in Project Euclid: 19 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60G55: Point processes

Extreme value theory Poisson processes max-stable processes prediction time series stationary processes


Davis, Richard A.; Resnick, Sidney I. Prediction of Stationary Max-Stable Processes. Ann. Appl. Probab. 3 (1993), no. 2, 497--525. doi:10.1214/aoap/1177005435.

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