{
  "id": "math/0310262",
  "version": "v1",
  "published": "2003-10-17T10:47:25.000Z",
  "updated": "2003-10-17T10:47:25.000Z",
  "title": "Probabilistic representations of solutions to the heat equation",
  "authors": [
    "B. Rajeev",
    "S. Thangavelu"
  ],
  "comment": "12 pages",
  "journal": "Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 3, August 2003, pp. 321-332",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if $\\phi$ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition $\\phi$, is given by the convolution of $\\phi$ with the heat kernel (Gaussian density). Our results also extend the probabilistic representation of solutions of the heat equation to initial conditions that are arbitrary tempered distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-17T10:47:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heat equation",
      "probabilistic representation",
      "initial condition",
      "partial differential equations",
      "arbitrary tempered distributions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10262R"
    }
  }
}