{
  "id": "0802.1152",
  "version": "v4",
  "published": "2008-02-08T13:38:51.000Z",
  "updated": "2009-12-09T10:46:33.000Z",
  "title": "Hiding a drift",
  "authors": [
    "Miklós Rásonyi",
    "Walter Schachermayer",
    "Richard Warnung"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AOP469 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2009, Vol. 37, No. 6, 2459-2479",
  "doi": "10.1214/09-AOP469",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article we consider a Brownian motion with drift of the form \\[dS_t=\\mu_t dt+dB_t\\qquadfor t\\ge0,\\] with a specific nontrivial $(\\mu_t)_{t\\geq0}$, predictable with respect to $\\mathbb{F}^B$, the natural filtration of the Brownian motion $B=(B_t)_{t\\ge0}$. We construct a process $H=(H_t)_{t\\ge0}$, also predictable with respect to $\\mathbb{F}^B$, such that $((H\\cdot S)_t)_{t\\ge 0}$ is a Brownian motion in its own filtration. Furthermore, for any $\\delta>0$, we refine this construction such that the drift $(\\mu_t)_{t\\ge0}$ only takes values in $]\\mu-\\delta,\\mu+\\delta[$, for fixed $\\mu>0$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-12-09T10:46:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "60G44",
      "60G05",
      "60H10"
    ],
    "keywords": [
      "brownian motion",
      "specific nontrivial",
      "natural filtration",
      "construction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.1152R"
    }
  }
}