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February 2015 An exceptional max-stable process fully parameterized by its extremal coefficients
Kirstin Strokorb, Martin Schlather
Bernoulli 21(1): 276-302 (February 2015). DOI: 10.3150/13-BEJ567

Abstract

The extremal coefficient function (ECF) of a max-stable process $X$ on some index set $T$ assigns to each finite subset $A\subset T$ the effective number of independent random variables among the collection $\{X_{t}\}_{t\in A}$. We introduce the class of Tawn–Molchanov processes that is in a 1:1 correspondence with the class of ECFs, thus also proving a complete characterization of the ECF in terms of negative definiteness. The corresponding Tawn–Molchanov process turns out to be exceptional among all max-stable processes sharing the same ECF in that its dependency set is maximal w.r.t. inclusion. This entails sharp lower bounds for the finite dimensional distributions of arbitrary max-stable processes in terms of its ECF. A spectral representation of the Tawn–Molchanov process and stochastic continuity are discussed. We also show how to build new valid ECFs from given ECFs by means of Bernstein functions.

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Kirstin Strokorb. Martin Schlather. "An exceptional max-stable process fully parameterized by its extremal coefficients." Bernoulli 21 (1) 276 - 302, February 2015. https://doi.org/10.3150/13-BEJ567

Information

Published: February 2015
First available in Project Euclid: 17 March 2015

zbMATH: 1323.60075
MathSciNet: MR3322319
Digital Object Identifier: 10.3150/13-BEJ567

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

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Vol.21 • No. 1 • February 2015
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