An exceptional max-stable process fully parameterized by its extremal coefficients
An exceptional max-stable process fully parameterized by its extremal coefficients
复制标题
一种特殊的最大稳定过程，由其极值系数完全参数化
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Martin Schlather
中科院分区：
文献类型：
--
作者：
K. Strokorb;Martin Schlather
某指标集T上极大稳定过程X的极值系数函数赋予每个有限子集A⊂T集合{XT}t∈A中独立随机变量的有效个数.我们引入了与极大稳定过程类1：1对应的Tawn-Molchanov过程类，从而证明了极大稳定过程的负定性的完全刻画.在所有共享相同ECF的极大稳定过程中，对应的Tawn-Molchanov过程是例外的，因为它的依赖集是最大的W.r.t。包容性。这就得到了任意极大稳定过程关于其ECF的有限维分布的精确下界。讨论了Tawn-Molchanov过程的谱表示和随机连续性。我们还展示了如何通过Bernstein函数从给定的ECF构造新的有效ECF。
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.