{
  "id": "0903.3594",
  "version": "v2",
  "published": "2009-03-20T19:25:52.000Z",
  "updated": "2009-09-18T17:59:14.000Z",
  "title": "On the Structure and Representations of Max--Stable Processes",
  "authors": [
    "Yizao Wang",
    "Stilian A. Stoev"
  ],
  "comment": "40 pages. Minor changes. Technical Report 487, Department of Statistics, University of Michigan",
  "categories": [
    "math.PR"
  ],
  "abstract": "We develop classification results for max--stable processes, based on their spectral representations. The structure of max--linear isometries and minimal spectral representations play important roles. We propose a general classification strategy for measurable max--stable processes based on the notion of co--spectral functions. In particular, we discuss the spectrally continuous--discrete, the conservative--dissipative, and positive--null decompositions. For stationary max--stable processes, the latter two decompositions arise from connections to non--singular flows and are closely related to the classification of stationary sum--stable processes. The interplay between the introduced decompositions of max--stable processes is further explored. As an example, the Brown-Resnick stationary processes, driven by fractional Brownian motions, are shown to be dissipative. A result on general Gaussian processes with stationary increments and continuous paths is obtained.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-18T17:59:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G52",
      "60G70",
      "37A50"
    ],
    "keywords": [
      "max-stable processes",
      "minimal spectral representations play important",
      "spectral representations play important roles",
      "stationary",
      "general classification strategy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.3594W"
    }
  }
}