{
  "id": "2101.06895",
  "version": "v1",
  "published": "2021-01-18T06:21:15.000Z",
  "updated": "2021-01-18T06:21:15.000Z",
  "title": "On the finiteness of moments of the exit time of planar Brownian motion from comb domains",
  "authors": [
    "Maher Boudabra",
    "Greg Markowsky"
  ],
  "categories": [
    "math.PR",
    "math.CV"
  ],
  "abstract": "A comb domain is defined to be the entire complex plain with a collection of vertical slits, symmetric over the real axis, removed. In this paper, we consider the question of determining whether the exit time of planar Brownian motion from such a domain has finite $p$-th moment. This question has been addressed before in relation to starlike domains, but these previous results do not apply to comb domains. Our main result is a sufficient condition on the location of the slits which ensures that the $p$-th moment of the exit time is finite. Several auxiliary results are also presented, including a construction of a comb domain whose exit time has infinite $p$-th moment for all $p \\geq 1/2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-18T06:21:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar brownian motion",
      "comb domain",
      "exit time",
      "th moment",
      "finiteness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}