{
  "id": "1307.4992",
  "version": "v1",
  "published": "2013-07-18T15:58:47.000Z",
  "updated": "2013-07-18T15:58:47.000Z",
  "title": "Cylindrical Fractional Brownian Motion in Banach Spaces",
  "authors": [
    "Elena Issoglio",
    "Markus Riedle"
  ],
  "comment": "29 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of cylindrical random variables and cylindrical measures. The developed stochastic integral for deterministic operator valued integrands is based on a series representation of the cylindrical fractional Brownian motion, which is analogous to the Karhunen-Lo\\`eve expansion for genuine stochastic processes. In the last part we apply our results to study the abstract stochastic Cauchy problem in a Banach space driven by cylindrical fractional Brownian motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-18T15:58:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60H05",
      "60H15",
      "28C20"
    ],
    "keywords": [
      "cylindrical fractional brownian motion",
      "abstract stochastic cauchy problem",
      "related stochastic integration theory",
      "deterministic operator valued integrands",
      "genuine stochastic processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.4992I"
    }
  }
}