{
  "id": "math/0702708",
  "version": "v2",
  "published": "2007-02-23T16:44:31.000Z",
  "updated": "2007-06-01T10:00:09.000Z",
  "title": "Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems",
  "authors": [
    "Tomasz Bojdecki",
    "Luis G. Gorostiza",
    "Anna Talarczyk"
  ],
  "comment": "11 pages; minor corrections and changes in notation",
  "journal": "Elect. Comm. in Probab. 12 (2007), 161-172",
  "doi": "10.1214/ECP.v12-1272",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study three self-similar, long-range dependence, Gaussian processes. The first one, with covariance \\int_0^{s\\wedge t} u^a [(t-u)^b+(s-u)^b]du, parameters a>-1, -1<b\\leq 1, |b|\\leq 1+a, corresponds to fractional Brownian motion for a=0, -1<b<1. The second one, with covariance (2-h)(s^h+t^h-[(s+t)^h +|s-t|^h]/2), parameter 0<h\\leq 4, corresponds to sub-fractional Brownian motion for 0<h<2. The third one, with covariance -(s^2\\log s + t^2\\log t -[(s+t)^2 \\log (s+t) +(s-t)^2 \\log |s-t|]/2), is related to the second one. These processes come from occupation time fluctuations of certain particle systems for some values of the parameters.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-06-01T10:00:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G18",
      "60J80"
    ],
    "keywords": [
      "sub-fractional brownian motion",
      "particle systems",
      "extensions",
      "covariance",
      "occupation time fluctuations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2708B"
    }
  }
}