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

作者：Strokorb Kirstin^*; Schlather Martin

来源：Bernoulli, 2015, 21(1): 276-302.

DOI：10.3150/13-BEJ567

• completely alternating
• dependency set
• extremal coefficient
• max-linear model
• max-stable process
• negative definite
• semigroup
• spectrally discrete
• Tawn-Molchanov process

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

• 出版日期2015-2