{
  "id": "1209.3263",
  "version": "v1",
  "published": "2012-09-14T17:18:34.000Z",
  "updated": "2012-09-14T17:18:34.000Z",
  "title": "Stochastic solutions of nonlinear PDE's and an extension of superprocesses",
  "authors": [
    "Rui Vilela Mendes"
  ],
  "comment": "11 pages. arXiv admin note: substantial text overlap with arXiv:1111.5504",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "Stochastic solutions provide new rigorous results for nonlinear PDE's and, through its local non-grid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions: MacKean's and superprocesses. However, when restricted to measures, superprocesses can only be used to generate solutions for a limited class of nonlinear PDE's. A new class of superprocesses, namely superprocesses on signed measures and on distributions, is proposed to extend the stochastic solution approach to a wider class of PDE's.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-14T17:18:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear pdes",
      "superprocesses",
      "stochastic solution approach",
      "local non-grid nature",
      "generate solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.3263V"
    }
  }
}