{
  "id": "2108.01746",
  "version": "v1",
  "published": "2021-08-03T20:53:18.000Z",
  "updated": "2021-08-03T20:53:18.000Z",
  "title": "Stochastic evolution equations driven by cylindrical stable noise",
  "authors": [
    "Tomasz Kosmala",
    "Markus Riedle"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove existence and uniqueness of a mild solution of a stochastic evolution equation driven by a standard $\\alpha$-stable cylindrical L\\'evy process defined on a Hilbert space for $\\alpha \\in (1,2)$. The coefficients are assumed to map between certain domains of fractional powers of the generator present in the equation. The solution is constructed as a weak limit of the Picard iteration using tightness arguments. Existence of strong solution is obtained by a general version of the Yamada--Watanabe theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-03T20:53:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G52",
      "60G51",
      "47D06"
    ],
    "keywords": [
      "stochastic evolution equations driven",
      "cylindrical stable noise",
      "cylindrical levy process",
      "stochastic evolution equation driven",
      "strong solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}