{
  "id": "2409.14753",
  "version": "v1",
  "published": "2024-09-23T07:05:24.000Z",
  "updated": "2024-09-23T07:05:24.000Z",
  "title": "On the Palm distribution of superposition of point processes",
  "authors": [
    "Mario Beraha",
    "Federico Camerlenghi"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Palm distributions are critical in the study of point processes. In the present paper we focus on a point process $\\Phi$ defined as the superposition, i.e., sum, of two independent point processes, say $\\Phi = \\Phi_1 + \\Phi_2$, and we characterize its Palm distribution. In particular, we show that the Palm distribution of $\\Phi$ admits a simple mixture representation depending only on the Palm distribution of $\\Phi_j$, as $j=1, 2$, and the associated moment measures. Extensions to the superposition of multiple point processes, and higher order Palm distributions, are treated analogously.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-23T07:05:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "superposition",
      "higher order palm distributions",
      "multiple point processes",
      "simple mixture representation",
      "independent point processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}