{
  "id": "2403.08754",
  "version": "v1",
  "published": "2024-03-13T17:51:57.000Z",
  "updated": "2024-03-13T17:51:57.000Z",
  "title": "Sticky-threshold diffusions, local time approximation and parameter estimation",
  "authors": [
    "Alexis Anagnostakis",
    "Sara Mazzonetto"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a class of high frequency path functionals of a diffusion with a sticky-oscillating-skew (SOS) threshold, including the case of a sticky-reflection, and establish convergence to the local time. This extends existing results on sticky, oscillating (regime-switching) and skew or reflecting diffusions in several directions. First, it considers any normalizing sequence $(u_n)_n $ that diverges slower than $n$. Second, it allows combinations of these features. Based on this, and an approximation of the occupation time, we devise consistent skew and stickiness parameter estimators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-13T17:51:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62F12",
      "60J55",
      "60J60"
    ],
    "keywords": [
      "local time approximation",
      "parameter estimation",
      "sticky-threshold diffusions",
      "high frequency path functionals",
      "devise consistent skew"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}