{
  "id": "1312.3314",
  "version": "v2",
  "published": "2013-12-11T20:49:40.000Z",
  "updated": "2014-11-28T04:18:06.000Z",
  "title": "Analytical expansions for parabolic equations",
  "authors": [
    "Matthew Lorig",
    "Stefano Pagliarani",
    "Andrea Pascucci"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP",
    "q-fin.CP"
  ],
  "abstract": "We consider the Cauchy problem associated with a general parabolic partial differential equation in $d$ dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as rigorous short-time error estimates. Using a boot-strapping technique, we also provide convergence results for arbitrarily large time intervals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-11T20:49:40.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-28T04:18:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic equations",
      "analytical expansions",
      "general parabolic partial differential equation",
      "arbitrarily large time intervals",
      "rigorous short-time error estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.3314L"
    }
  }
}