{
  "id": "1801.06772",
  "version": "v1",
  "published": "2018-01-21T06:09:25.000Z",
  "updated": "2018-01-21T06:09:25.000Z",
  "title": "Stochastic PDEs in $\\mathcal{S}^\\prime$ for SDEs driven by Lévy noise",
  "authors": [
    "Suprio Bhar",
    "Rajeev Bhaskaran",
    "Barun Sarkar"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article we show that a finite dimensional stochastic differential equation driven by a L\\'evy process can be formulated as a stochastic partial differential equation. We prove the existence and uniqueness of strong solutions of such stochastic PDEs. The solutions that we construct have the `translation invariance' property. The special case of this correspondence for diffusion processes was proved in [Rajeev, Translation invariant diffusion in the space of tempered distributions, Indian J. Pure Appl. Math. 44 (2013), no.~2, 231--258].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-21T06:09:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60H10",
      "60H15"
    ],
    "keywords": [
      "stochastic pdes",
      "lévy noise",
      "sdes driven",
      "finite dimensional stochastic differential equation",
      "dimensional stochastic differential equation driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}