{
  "id": "math/0505449",
  "version": "v1",
  "published": "2005-05-21T16:47:50.000Z",
  "updated": "2005-05-21T16:47:50.000Z",
  "title": "A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees",
  "authors": [
    "D. Blömker",
    "M. Romito",
    "R. Tribe"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The solutions to a large class of semi-linear parabolic PDEs are given in terms of expectations of suitable functionals of a tree of branching particles. A sufficient, and in some cases necessary, condition is given for the integrability of the stochastic representation, using a companion scalar PDE. In cases where the representation fails to be integrable a sequence of pruned trees is constructed, producing a approximate stochastic representations that in some cases converge, globally in time, to the solution of the original PDE.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-21T16:47:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "35Q30",
      "35K55",
      "35C99",
      "76M35",
      "60H30"
    ],
    "keywords": [
      "pruned branching trees",
      "probabilistic representation",
      "non-linear pdes",
      "companion scalar pde",
      "semi-linear parabolic pdes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5449B"
    }
  }
}