{
  "id": "1003.5276",
  "version": "v3",
  "published": "2010-03-27T08:31:51.000Z",
  "updated": "2010-03-31T13:36:11.000Z",
  "title": "Composition of processes and related partial differential equations",
  "authors": [
    "Mirko D'Ovidio",
    "Enzo Orsingher"
  ],
  "comment": "32 pages",
  "journal": "Journal of Theoretical Probability, 24, (2011), 342 - 375",
  "doi": "10.1007/s10959-010-0284-9",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper different types of compositions involving independent fractional Brownian motions B^j_{H_j}(t), t>0, j=1,$ are examined. The partial differential equations governing the distributions of I_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|), t>0 and J_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|^{1/H_1}), t>0 are derived by different methods and compared with those existing in the literature and with those related to B^1(|B^2_{H_2}(t)|), t>0. The process of iterated Brownian motion I^n_F(t), t>0 is examined in detail and its moments are calculated. Furthermore for J^{n-1}_F(t)=B^1_{H}(|B^2_H(...|B^n_H(t)|^{1/H}...)|^{1/H}), t>0 the following factorization is proved J^{n-1}_F(t)=\\prod_{j=1}^{n} B^j_{\\frac{H}{n}}(t), t>0. A series of compositions involving Cauchy processes and fractional Brownian motions are also studied and the corresponding non-homogeneous wave equations are derived.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-03-31T13:36:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60J60",
      "26A33"
    ],
    "keywords": [
      "related partial differential equations",
      "composition",
      "independent fractional brownian motions",
      "partial differential equations governing",
      "corresponding non-homogeneous wave equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.5276D"
    }
  }
}