{
  "id": "1403.1215",
  "version": "v1",
  "published": "2014-03-05T18:36:42.000Z",
  "updated": "2014-03-05T18:36:42.000Z",
  "title": "Example of a Gaussian self-similar field with stationary rectangular increments that is not a fractional Brownian sheet",
  "authors": [
    "Vitalii Makogin",
    "Yuliya Mishura"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider anisotropic self-similar random fields, in particular, the fractional Brownian sheet. This Gaussian field is an extension of fractional Brownian motion. We prove some properties of covariance function for self-similar fields with rectangular increments. Using Lamperti transformation we obtain properties of covariance function for the corresponding stationary fields. We present an example of a Gaussian self-similar field with stationary rectangular increments that is not a fractional Brownian sheet.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-05T18:36:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G60",
      "60G18",
      "60G22"
    ],
    "keywords": [
      "fractional brownian sheet",
      "stationary rectangular increments",
      "gaussian self-similar field",
      "covariance function",
      "anisotropic self-similar random fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.1215M"
    }
  }
}