{
  "id": "1001.1336",
  "version": "v2",
  "published": "2010-01-08T18:57:07.000Z",
  "updated": "2019-09-01T16:04:55.000Z",
  "title": "Time to reach the maximum for a random acceleration process",
  "authors": [
    "Satya N. Majumdar",
    "Alberto Rosso",
    "Andrea Zoia"
  ],
  "comment": "17 pages, 5 figures Typo in Eq. (B.11) corrected",
  "journal": "J. Phys. A: Math. Theor. 43, 115001 (2010)",
  "doi": "10.1088/1751-8113/43/11/115001",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the random acceleration model, which is perhaps one of the simplest, yet nontrivial, non-Markov stochastic processes, and is key to many applications. For this non-Markov process, we present exact analytical results for the probability density $p(t_m|T)$ of the time $t_m$ at which the process reaches its maximum, within a fixed time interval $[0,T]$. We study two different boundary conditions, which correspond to the process representing respectively (i) the integral of a Brownian bridge and (ii) the integral of a free Brownian motion. Our analytical results are also verified by numerical simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-08T18:57:07.000Z",
      "comment": "17 pages, 5 figures"
    },
    {
      "version": "v2",
      "updated": "2019-09-01T16:04:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random acceleration process",
      "free brownian motion",
      "random acceleration model",
      "non-markov stochastic processes",
      "process reaches"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Mar",
      "volume": 43,
      "number": 11,
      "pages": 115001,
      "publisher": "IOP"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JPhA...43k5001M"
    }
  }
}