{
  "id": "1402.5864",
  "version": "v1",
  "published": "2014-02-24T15:52:16.000Z",
  "updated": "2014-02-24T15:52:16.000Z",
  "title": "A necessary and sufficient condition for the non-trivial limit of the derivative martingale in a branching random walk",
  "authors": [
    "Xinxin Chen"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a branching random walk on the line. Biggins and Kyprianou [6] proved that, in the boundary case, the associated derivative martingale converges almost surly to a finite nonnegative limit, whose law serves as a fixed point of a smoothing transformation (Mandelbrot's cascade). In the present paper, we give a necessary and sufficient condition for the non-triviality of this limit and establish a Kesten-Stigum-like result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-24T15:52:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "branching random walk",
      "sufficient condition",
      "non-trivial limit",
      "boundary case",
      "associated derivative martingale converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.5864C"
    }
  }
}