{
  "id": "0908.0356",
  "version": "v1",
  "published": "2009-08-03T22:12:48.000Z",
  "updated": "2009-08-03T22:12:48.000Z",
  "title": "On linear evolution equations with cylindrical Lévy noise",
  "authors": [
    "Enrico Priola",
    "Jerzy Zabczyk"
  ],
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We study an infinite-dimensional Ornstein-Uhlenbeck process $(X_t)$ in a given Hilbert space $H$. This is driven by a cylindrical symmetric L\\'evy process without a Gaussian component and taking values in a Hilbert space $U$ which usually contains $H$. We give if and only if conditions under which $X_t$ takes values in $H$ for some $t>0$ or for all $t>0$. Moreover, we prove irreducibility for $(X_t)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-03T22:12:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D07",
      "60H15",
      "60J75",
      "35R60"
    ],
    "keywords": [
      "linear evolution equations",
      "cylindrical lévy noise",
      "hilbert space",
      "infinite-dimensional ornstein-uhlenbeck process",
      "cylindrical symmetric levy process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.0356P"
    }
  }
}