{
  "id": "1808.03407",
  "version": "v1",
  "published": "2018-08-10T04:17:28.000Z",
  "updated": "2018-08-10T04:17:28.000Z",
  "title": "A note on the critical barrier for the survival of $α-$stable branching random walk with absorption",
  "authors": [
    "Jingning Liu",
    "Mei Zhang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a branching random walk with an absorbing barrier, where the step of the associated one-dimensional random walk is in the domain of attraction of an $\\alpha$-stable law with $1<\\alpha<2$. We shall prove that there is a barrier $an^{\\frac{1}{1+\\alpha}}$ and a critical value $a_\\alpha$ such that if $a<a_\\alpha$, then the process dies; if $a>a_\\alpha$, then the process survives. The results generalize previous results in literature for the case $\\alpha=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-10T04:17:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable branching random walk",
      "critical barrier",
      "absorption",
      "associated one-dimensional random walk",
      "process dies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}