The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 3, Number 2 (1993), 497-525.
Prediction of Stationary Max-Stable Processes
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.
Ann. Appl. Probab., Volume 3, Number 2 (1993), 497-525.
First available in Project Euclid: 19 April 2007
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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. https://projecteuclid.org/euclid.aoap/1177005435