{
  "id": "2401.03842",
  "version": "v1",
  "published": "2024-01-08T12:09:05.000Z",
  "updated": "2024-01-08T12:09:05.000Z",
  "title": "Branching Processes with Immigration in a Random Environment -- the Grincevičius--Grey setup",
  "authors": [
    "Peter Kevei"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We determine the tail asymptotics of the stationary distribution of a branching process with immigration in a random environment, when the immigration distribution dominates the offspring distribution. The assumptions are the same as in the Grincevi\\v{c}ius--Grey theorem for the stochastic recurrence equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-08T12:09:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60F05"
    ],
    "keywords": [
      "random environment",
      "branching process",
      "grincevičius-grey setup",
      "immigration distribution dominates",
      "stochastic recurrence equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}