{
  "id": "1711.06447",
  "version": "v1",
  "published": "2017-11-17T08:05:15.000Z",
  "updated": "2017-11-17T08:05:15.000Z",
  "title": "Renormalization of local times of super-Brownian motion",
  "authors": [
    "Jieliang Hong"
  ],
  "comment": "49 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "For the local time $L_t^x$ of super-Brownian motion $X$ starting from $\\delta_0$, we study its asymptotic behavior as $x\\to 0$. In $d=3$, we find a normalization $\\psi(x)=(1/(2\\pi^2) \\log (1/|x|))^{1/2}$ such that $(L_t^x-1/(2\\pi|x|))/\\psi(x)$ converges in distribution to standard normal as $x\\to 0$. In $d=2$, we show that $L_t^x-(1/\\pi)\\log (1/|x|)$ converges a.s. as $x\\to 0$. We also consider general initial conditions and get similar renormalization results. The behavior of the local time allows us to derive a second order term in the asymptotic behavior of a related semilinear elliptic equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-17T08:05:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J68"
    ],
    "keywords": [
      "local time",
      "super-brownian motion",
      "asymptotic behavior",
      "related semilinear elliptic equation",
      "general initial conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}