{
  "id": "2202.09158",
  "version": "v1",
  "published": "2022-02-18T12:19:04.000Z",
  "updated": "2022-02-18T12:19:04.000Z",
  "title": "Description of random fields by systems of conditional distributions",
  "authors": [
    "L. A. Khachatryan"
  ],
  "comment": "26 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we consider the direct and inverse problems of the description of random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions. In the majority of cases, we provide necessary and sufficient conditions for the system to be a conditional distribution of a (unique) random field. The exception is Dobrushin-type systems for which only sufficient conditions are known. Also, we discuss the possible applications of the considered systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-18T12:19:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G60",
      "60E05",
      "60J99"
    ],
    "keywords": [
      "random field",
      "conditional distribution",
      "description",
      "sufficient conditions",
      "inverse problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}