{
  "id": "1101.3915",
  "version": "v1",
  "published": "2011-01-20T14:36:11.000Z",
  "updated": "2011-01-20T14:36:11.000Z",
  "title": "A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process",
  "authors": [
    "Peter J. Thomas"
  ],
  "comment": "15 pages, 1 figure",
  "journal": "J. Appl. Probab. Volume 48, Number 2 (2011), 420-434",
  "doi": "10.1239/jap/1308662636",
  "categories": [
    "math.PR",
    "q-bio.NC"
  ],
  "abstract": "We prove that the first passage time density $\\rho(t)$ for an Ornstein-Uhlenbeck process $X(t)$ obeying $dX=-\\beta X dt + \\sigma dW$ to reach a fixed threshold $\\theta$ from a suprathreshold initial condition $x_0>\\theta>0$ has a lower bound of the form $\\rho(t)>k \\exp\\left[-p e^{6\\beta t}\\right]$ for positive constants $k$ and $p$ for times $t$ exceeding some positive value $u$. We obtain explicit expressions for $k, p$ and $u$ in terms of $\\beta$, $\\sigma$, $x_0$ and $\\theta$, and discuss application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-20T14:36:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J70",
      "92C20"
    ],
    "keywords": [
      "first passage time density",
      "suprathreshold ornstein-uhlenbeck process",
      "lower bound",
      "forced stochastic leaky integrate-and-fire",
      "stochastic leaky integrate-and-fire model neurons"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}