{
  "id": "1905.10165",
  "version": "v1",
  "published": "2019-05-24T11:53:21.000Z",
  "updated": "2019-05-24T11:53:21.000Z",
  "title": "Estimation of Stopping Times for Stopped Self-Similar Random Processes",
  "authors": [
    "Viktor Schulmann"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $X=(X_t)_{t\\geq 0}$ be a known process and $T$ an unknown random time independent of $X$. Our goal is to derive the distribution of $T$ based on an iid sample of $X_T$. Belomestny and Schoenmakers (2015) propose a solution based the Mellin transform in case where $X$ is a Brownian motion. Applying their technique we construct a non-parametric estimator for the density of $T$ for a self-similar one-dimensional process $X$. We calculate the minimax convergence rate of our estimator in some examples with a particular focus on Bessel processes where we also show asymptotic normality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-24T11:53:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62G07",
      "62G20",
      "60G18",
      "60G40"
    ],
    "keywords": [
      "stopped self-similar random processes",
      "stopping times",
      "estimation",
      "unknown random time independent",
      "self-similar one-dimensional process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}