{
  "id": "2403.12610",
  "version": "v1",
  "published": "2024-03-19T10:24:18.000Z",
  "updated": "2024-03-19T10:24:18.000Z",
  "title": "Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes",
  "authors": [
    "Petr Čoupek",
    "Pavel Kříž",
    "Bohdan Maslowski"
  ],
  "comment": "22 pages, 6 figures",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "In this paper, we study parameter identification for solutions to (possibly non-linear) SDEs driven by additive Rosenblatt process and singularity of the induced laws on the path space. We propose a joint estimator for the drift parameter, diffusion intensity, and Hurst index that can be computed from discrete-time observations with a bounded time horizon and we prove its strong consistency (as well as the speed of convergence) under in-fill asymptotics with a fixed time horizon. As a consequence of this strong consistency, singularity of measures generated by the solutions with different drifts is shown. This results in the invalidity of a Girsanov-type theorem for Rosenblatt processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-19T10:24:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "62M09"
    ],
    "keywords": [
      "sdes driven",
      "path space",
      "parameter estimation",
      "singularity",
      "strong consistency"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}