{
  "id": "1501.00692",
  "version": "v1",
  "published": "2015-01-04T16:26:04.000Z",
  "updated": "2015-01-04T16:26:04.000Z",
  "title": "A simple construction of the continuum parabolic Anderson model on $\\mathbf{R}^2$",
  "authors": [
    "Martin Hairer",
    "Cyril Labbé"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We propose a simple construction of the solution to the continuum parabolic Anderson model on $\\mathbf{R}^2$ which does not rely on any elaborate arguments and makes extensive use of the linearity of the equation. A logarithmic renormalisation is required to counterbalance the divergent product appearing in the equation. Furthermore, we use time-dependent weights in our spaces of distributions in order to construct the solution on the unbounded space $\\mathbf{R}^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-04T16:26:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuum parabolic anderson model",
      "simple construction",
      "time-dependent weights",
      "elaborate arguments",
      "divergent product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150100692H"
    }
  }
}