{
  "id": "1610.03575",
  "version": "v1",
  "published": "2016-10-12T01:41:13.000Z",
  "updated": "2016-10-12T01:41:13.000Z",
  "title": "On Seneta-Heyde Scaling for a stable branching random walk",
  "authors": [
    "Hui He",
    "Jingning Liu",
    "Mei Zhang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a discrete-time branching random walk in the boundary case, where the associated random walk is in the domain of attraction of an $\\alpha$-stable law with $1<\\alpha<2$. We prove that the derivative martingale $D_n$ converges to a non-trivial limit $D_\\infty$ under some regular conditions. We also study the additive martingale $W_n$, and prove $n^\\frac{1}{\\alpha}W_n$ converges in probability to a constant multiple of $D_\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-12T01:41:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable branching random walk",
      "seneta-heyde scaling",
      "discrete-time branching random walk",
      "constant multiple",
      "associated random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}