{
  "id": "2401.07860",
  "version": "v1",
  "published": "2024-01-15T17:50:46.000Z",
  "updated": "2024-01-15T17:50:46.000Z",
  "title": "Galton-Watson theta-processes in a varying environment",
  "authors": [
    "Serik Sagitov",
    "Yerakhmet Zhumayev"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a special class of Galton-Watson theta-processes in a varying environment fully defined by four parameters, with two of them $(\\theta,r)$ being fixed over time $n$, and the other two $(a_n,c_n)$ characterizing the altering reproduction laws. We establish a sequence of transparent limit theorems for the theta-processes with possibly defective reproduction laws. These results may serve as a stepping stone towards incisive general results for the Galton-Watson processes in a varying environment.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-15T17:50:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80"
    ],
    "keywords": [
      "varying environment",
      "galton-watson theta-processes",
      "transparent limit theorems",
      "incisive general results",
      "altering reproduction laws"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}