{
  "id": "2102.01616",
  "version": "v1",
  "published": "2021-02-02T17:18:27.000Z",
  "updated": "2021-02-02T17:18:27.000Z",
  "title": "Divergence of an integral of a process with small ball estimate",
  "authors": [
    "Yuliya Mishura",
    "Nakahiro Yoshida"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "The paper contains sufficient conditions on the function $f$ and the stochastic process $X$ that supply the rate of divergence of the integral functional $\\int_0^Tf(X_t)^2dt$ at the rate $T^{1-\\epsilon}$ as $T\\to\\infty$ for every $\\epsilon>0$. These conditions include so called small ball estimates which are discussed in detail. Statistical applications are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-02T17:18:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small ball estimate",
      "divergence",
      "paper contains sufficient conditions",
      "stochastic process",
      "integral functional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}