{
  "id": "2407.05514",
  "version": "v1",
  "published": "2024-07-07T23:21:13.000Z",
  "updated": "2024-07-07T23:21:13.000Z",
  "title": "Exact convergence rates to derivatives of local time for some self-similar Gaussian processes",
  "authors": [
    "Minhao Hong"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, for some $d-$dimensional Gaussian processes \\[X=\\big\\{X_t=(X^1_t,\\cdots,X^d_t):t\\ge0\\big\\},\\] whose components are i.i.d. $1-$dimensional self-similar Gaussian process with Hurst index $H\\in(0,1)$, we consider the asymptotic behavior of approximation of its $\\boldsymbol{k}-$th derivatives of local time under certain mild conditions, where $\\boldsymbol{k}=(k_1,\\cdots,k_d)$ and $k_\\ell$'s are non-negative real numbers. We will give a derivative version of the limit theorems for functional of Gaussian processes and use this result to get the asymptotic behaviors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-07T23:21:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact convergence rates",
      "local time",
      "derivative",
      "dimensional self-similar gaussian process",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}