{
  "id": "1007.1738",
  "version": "v2",
  "published": "2010-07-10T19:39:40.000Z",
  "updated": "2011-09-06T09:37:27.000Z",
  "title": "Moments, moderate and large deviations for a branching process in a random environment",
  "authors": [
    "Chunmao Huang",
    "Quansheng Liu"
  ],
  "journal": "Stochastic Processes and their Applications 122 (2012) 522-545",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $(Z_{n})$ be a supercritical branching process in a random environment $\\xi $, and $W$ be the limit of the normalized population size $Z_{n}/\\mathbb{E}[Z_{n}|\\xi ]$. We show large and moderate deviation principles for the sequence $\\log Z_{n}$ (with appropriate normalization). For the proof, we calculate the critical value for the existence of harmonic moments of $W$, and show an equivalence for all the moments of $Z_{n}$. Central limit theorems on $W-W_n$ and $\\log Z_n$ are also established.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-06T09:37:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60K37",
      "60F10"
    ],
    "keywords": [
      "random environment",
      "branching process",
      "large deviations",
      "central limit theorems",
      "moderate deviation principles"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.1738H"
    }
  }
}