{
  "id": "1704.07481",
  "version": "v1",
  "published": "2017-04-24T22:20:36.000Z",
  "updated": "2017-04-24T22:20:36.000Z",
  "title": "Strong approximation of density dependent Markov chains on bounded domains",
  "authors": [
    "Enrico Bibbona",
    "Roberta Sirovich"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Density dependent families of Markov chains, such as the stochastic models of mass-action chemical kinetics, converge for large values of the indexing parameter $N$ to deterministic systems of differential equations (Kurtz, 1970). Moreover for moderate $N$ they can be strongly approximated by paths of a diffusion process (Kurtz, 1976). Such an approximation however fails if the state space is bounded (at zero or at a constant maximum level due to conservation of mass) and if the process visits the boundaries with non negligible probability. We present a strong approximation by a jump-diffusion process which is robust to this event. The result is illustrated with a particularly hard case study.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-24T22:20:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J28",
      "60J70",
      "60J75",
      "60F15",
      "92C42"
    ],
    "keywords": [
      "density dependent markov chains",
      "strong approximation",
      "bounded domains",
      "density dependent families",
      "constant maximum level"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}