{
  "id": "2102.10572",
  "version": "v1",
  "published": "2021-02-21T10:00:59.000Z",
  "updated": "2021-02-21T10:00:59.000Z",
  "title": "Limit theorems on counting measures for a branching random walk with immigration in a random environment",
  "authors": [
    "Mengxue Li",
    "Chuanmao Huang",
    "Xiaoqiang Wang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a branching random walk with immigration in a random environment, where the environment is a stationary and ergodic sequence indexed by time. We focus on the asymptotic properties of the sequence of measures $(Z_n)$ that count the number of particles of generation $n$ located in a Borel set of real line. In the present work, a series of limit theorems related to the above counting measures are established, including a central limit theorem, a moderate deviation principle and a large deviation result as well as a convergence theorem of the free energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-21T10:00:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "branching random walk",
      "random environment",
      "counting measures",
      "immigration",
      "central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}