{
  "id": "1307.6050",
  "version": "v1",
  "published": "2013-07-23T12:57:52.000Z",
  "updated": "2013-07-23T12:57:52.000Z",
  "title": "Limit theorems for excursion sets of stationary random fields",
  "authors": [
    "Evgeny Spodarev"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We give an overview of the recent asymptotic results on the geometry of excursion sets of stationary random fields. Namely, we cover a number of limit theorems of central type for the volume of excursions of stationary (quasi--, positively or negatively) associated random fields with stochastically continuous realizations for a fixed excursion level. This class includes in particular Gaussian, Poisson shot noise, certain infinitely divisible, $\\alpha$--stable and max--stable random fields satisfying some extra dependence conditions. Functional limit theorems (with the excursion level being an argument of the limiting Gaussian process) are reviewed as well. For stationary isotropic $C^1$--smooth Gaussian random fields similar results are available also for the surface area of the excursion set. Statistical tests of Gaussianity of a random field which are of importance to real data analysis as well as results for an increasing excursion level round up the paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-23T12:57:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary random fields",
      "excursion set",
      "limit theorems",
      "excursion level",
      "gaussian random fields similar results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.6050S"
    }
  }
}