{
  "id": "1209.2993",
  "version": "v3",
  "published": "2012-09-13T19:05:22.000Z",
  "updated": "2013-03-15T19:42:14.000Z",
  "title": "Small Kappa Asymptotics of the Almost Sure Lyapunov Exponent for the Continuum Parabolic Anderson Model",
  "authors": [
    "Michael Rael"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that the almost sure Lyapunov exponent \\lambda(\\kappa) of the continuous space Parabolic Anderson Model is bounded above by $c_u \\kappa^{1/3}$ as $\\kappa\\downarrow0$ under mild regularity conditions. This bound of the same order of the previously proven lower bound, $\\lambda(\\kappa) \\ge c_l \\kappa^{1/3}$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-03-15T19:42:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuum parabolic anderson model",
      "sure lyapunov exponent",
      "small kappa asymptotics",
      "space parabolic anderson model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2993R"
    }
  }
}