{
  "id": "1807.11418",
  "version": "v1",
  "published": "2018-07-30T16:11:13.000Z",
  "updated": "2018-07-30T16:11:13.000Z",
  "title": "Variational solutions of stochastic partial differential equations with cylindrical Lévy noise",
  "authors": [
    "Tomasz Kosmala",
    "Markus Riedle"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, the existence of a unique solution in the variational approach to the stochastic evolution equation $dX(t) = F(X(t))dt + G(X(t)) dL(t)$ driven by a cylindrical L\\'evy process $L$ is established. The coefficients $F$ and $G$ are assumed to satisfy the usual monotonicity and coercivity conditions. In the case of a cylindrical L\\'evy process with finite second moments, we derive the result without further assumptions. For the case of cylindrical L\\'evy processes without finite moments, we consider a subclass containing numerous examples from the literature. Deriving the existence result in the latter case requires a careful analysis of the jumps of cylindrical L\\'evy processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-30T16:11:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G51",
      "60G20",
      "28A35"
    ],
    "keywords": [
      "stochastic partial differential equations",
      "cylindrical levy process",
      "cylindrical lévy noise",
      "variational solutions",
      "stochastic evolution equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}