{
  "id": "1107.5136",
  "version": "v3",
  "published": "2011-07-26T08:54:55.000Z",
  "updated": "2011-10-17T13:40:26.000Z",
  "title": "On Max-Stable Processes and the Functional D-Norm",
  "authors": [
    "Stefan Aulbach",
    "Michael Falk",
    "Martin Hofmann"
  ],
  "comment": "22 pages",
  "doi": "10.1007/s10687-012-0160-3",
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence. The distribution function G of a continuous max-stable process on [0,1] is introduced and it is shown that G can be represented via a norm on functional space, called D-norm. This is in complete accordance with the multivariate case and leads to the definition of functional generalized Pareto distributions (GPD) W. These satisfy W=1+log(G) in their upper tails, again in complete accordance with the uni- or multivariate case. Applying this framework to copula processes we derive characterizations of the domain of attraction condition for copula processes in terms of tail equivalence with a functional GPD. \\delta-neighborhoods of a functional GPD are introduced and it is shown that these are characterized by a polynomial rate of convergence of functional extremes, which is well-known in the multivariate case.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-17T13:40:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G70"
    ],
    "keywords": [
      "functional d-norm",
      "max-stable processes",
      "multivariate case",
      "functional gpd",
      "copula processes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5136A"
    }
  }
}