On max-stable processes and the functional D-norm
On max-stable processes and the functional D-norm
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关于最大稳定过程和函数 D 范数
DOI：
10.1007/s10687-012-0160-3
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发表时间：
2013
期刊：
影响因子：
1.3
通讯作者：
Hofmann
中科院分区：
文献类型：
--
作者：
Aulbach;Hofmann
介绍了紧区间上连续函数空间中极值理论的一些数学框架，并给出了基本的定义和工具。[0，1]上的连续极大稳定过程的“分布函数”G可以用函数空间上的一个范数表示，称为D-范数。这种设置与多元情形的高度一致性导致了随机过程的函数吸引域方法的引入，该方法比通常的基于弱收敛的方法更具一般性。我们还引入了“逗留时间变换”的概念，并比较了函数空间上的几种收敛类型。同样，完全按照单变量或多变量的情况，现在可以在上尾得到泛函广义帕累托分布WviaW= 1 + Log(G)。特别地，这使得我们能够得到Copula过程的吸引条件的函数域的特征。
We introduce some mathematical framework for extreme value theory in the space of continuous functions on compact intervals and provide basic definitions and tools. Continuous max-stable processes on [0, 1] are characterized by their “distribution functions”Gwhich can be represented via a norm on function space, calledD-norm. The high conformity of this setup with the multivariate case leads to the introduction of a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence. We also introduce the concept of “sojourn time transformation” and compare several types of convergence on function space. Again in complete accordance with the uni- or multivariate case it is now possible to get functional generalized Pareto distributions (GPD)WviaW= 1 + log(G) in the upper tail. In particular, this enables us to derive characterizations of the functional domain of attraction condition for copula processes.