{
  "id": "0705.0168",
  "version": "v2",
  "published": "2007-05-01T20:26:33.000Z",
  "updated": "2007-05-09T20:25:31.000Z",
  "title": "Brownian subordinators and fractional Cauchy problems",
  "authors": [
    "Boris Baeumer",
    "Mark M. Meerschaert",
    "Erkan Nane"
  ],
  "comment": "18 pages, minor spelling corrections",
  "journal": "Trans. Amer. Math. Soc.361 (2009), 3915-3930.",
  "doi": "10.1090/S0002-9947-09-04678-9",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "A Brownian time process is a Markov process subordinated to the absolute value of an independent one-dimensional Brownian motion. Its transition densities solve an initial value problem involving the square of the generator of the original Markov process. An apparently unrelated class of processes, emerging as the scaling limits of continuous time random walks, involve subordination to the inverse or hitting time process of a classical stable subordinator. The resulting densities solve fractional Cauchy problems, an extension that involves fractional derivatives in time. In this paper, we will show a close and unexpected connection between these two classes of processes, and consequently, an equivalence between these two families of partial differential equations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-05-09T20:25:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60J60",
      "26A33"
    ],
    "keywords": [
      "fractional cauchy problems",
      "brownian subordinators",
      "independent one-dimensional brownian motion",
      "original markov process",
      "initial value problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0168B"
    }
  }
}