{
  "id": "1206.6789",
  "version": "v1",
  "published": "2012-06-28T18:33:31.000Z",
  "updated": "2012-06-28T18:33:31.000Z",
  "title": "Moment densities of super-Brownian motion, and a Harnack estimate for a class of X-harmonic functions",
  "authors": [
    "Thomas S. Salisbury",
    "A. Deniz Sezer"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper features a comparison inequality for the densities of the moment measures of super-Brownian motion. These densities are defined recursively for each $n \\ge 1$ in terms of the Poisson and Green's kernels, hence can be analyzed using the techniques of classical potential theory. When $n = 1$, the moment density is equal to the Poisson kernel, and the comparison is simply the classical inequality of Harnack. For $n > 1$ we find that the constant in the comparison inequality grows at most exponentially with $n$. We apply this to a class of $X$-harmonic functions $H^\\nu$ of super-Brownian motion, introduced by Dynkin. We show that for a.e. $H^\\nu$ in this class, $H^\\nu(\\mu)<\\infty$ for every $\\mu$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-28T18:33:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J68"
    ],
    "keywords": [
      "super-brownian motion",
      "moment density",
      "x-harmonic functions",
      "harnack estimate",
      "comparison inequality grows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.6789S"
    }
  }
}