{
  "id": "2204.10654",
  "version": "v1",
  "published": "2022-04-22T11:54:16.000Z",
  "updated": "2022-04-22T11:54:16.000Z",
  "title": "On functional limit theorems for branching processes with dependent immigration",
  "authors": [
    "Sadillo Sharipov"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we consider a triangular array of branching processes with non-stationary immigration. We prove a weak convergence of properly normalized branching processes with immigration to deterministic function under assumption that immigration is rowwise $\\psi-$mixing and the offspring mean tends to its critical value 1, immigration mean and variance controlled by regularly varying functions. Moreover, we obtain a fluctuation limit theorem for branching process with immigration when immigration is $m-$dependent where $m$ may tend to infinity with the row index at a certain rate. In this case the limiting process is a time-changed Wiener process. Our results extend and improve the previous known results in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-22T11:54:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "62F12"
    ],
    "keywords": [
      "branching process",
      "functional limit theorems",
      "dependent immigration",
      "fluctuation limit theorem",
      "results extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}