{
  "id": "1903.06157",
  "version": "v1",
  "published": "2019-03-14T17:58:15.000Z",
  "updated": "2019-03-14T17:58:15.000Z",
  "title": "Fecundity regulation in a spatial birth-and-death process",
  "authors": [
    "Viktor Bezborodov",
    "Luca Di Persio",
    "Dmitri Finkelshtein",
    "Yuri Kondratiev",
    "Oleksandr Kutoviy"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a Markov birth-and-death process on a space of locally finite configurations, which describes an ecological model with a density dependent fecundity regulation mechanism. We establish existence and uniqueness of this process and analyze its properties. In particular, we show global time-space boundedness of the population density and, using a constructed Foster-Lyapunov-type function, we study return times to certain level sets of tempered configurations. We find also sufficient conditions that the degenerate invariant distribution is unique for the considered process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-14T17:58:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "60J25",
      "82C21"
    ],
    "keywords": [
      "spatial birth-and-death process",
      "density dependent fecundity regulation mechanism",
      "global time-space boundedness",
      "degenerate invariant distribution",
      "study return times"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}