{
  "id": "2407.05252",
  "version": "v1",
  "published": "2024-07-07T03:59:40.000Z",
  "updated": "2024-07-07T03:59:40.000Z",
  "title": "The multiple birth properties of multi-type Markov branching processes",
  "authors": [
    "Junping Li",
    "Wanting Zhang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can reveal the multiple birth characteristics. Then the joint probability distribution of multiple birth of multi-type Markov branching process until any time $t$ is obtained by using the new process. Furthermore, the probability distribution of multiple birth until the extinction of the process is also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-07T03:59:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-type markov branching process",
      "multiple birth properties",
      "multi-dimensional markov process",
      "multiple birth characteristics",
      "joint probability distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}