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An exceptional max-stable process fully parameterized by its extremal coefficients

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

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Abstract

The extremal coefficient function (ECF) of a max-stable process X on some index set T assigns to each finite subset A⊂T the effective number of independent random variables among the collection {Xt}t∈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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Completely alternating; Dependency set; Extremal coefficient; Max-linear model; Max-stable process; Negative definite; Semigroup; Spectrally discrete; Tawn–Molchanov process
Publisher: Bernoulli Society for Mathematical Statistics and Probability
ISSN: 1350-7265
Funders: DFG (RTG1023)
Date of First Compliant Deposit: 6 January 2017
Date of Acceptance: 24 September 2013
Last Modified: 13 Mar 2019 12:33
URI: http://orca.cf.ac.uk/id/eprint/97222

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