{
  "id": "2207.03312",
  "version": "v1",
  "published": "2022-07-07T14:16:43.000Z",
  "updated": "2022-07-07T14:16:43.000Z",
  "title": "On the specific relative entropy between martingale diffusions on the line",
  "authors": [
    "Julio Backhoff-Veraguas",
    "Clara Unterberger"
  ],
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "The specific relative entropy, introduced by N. Gantert, allows to quantify the discrepancy between the laws of potentially mutually singular measures. It appears naturally as the large deviations rate function in a randomized version of Donsker's invariance principle, as well as in a novel transport-information inequality recently derived by H. Foellmer. A conjecture, put forward by the aforementioned authors, concerns a closed form expression for the specific relative entropy between continuous martingale laws in terms of their quadratic variations. We provide a first partial result in this direction, by establishing this conjecture in the case of well-behaved martingale diffusions on the line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-07T14:16:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "specific relative entropy",
      "large deviations rate function",
      "first partial result",
      "novel transport-information inequality",
      "donskers invariance principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}