{
  "id": "1801.01584",
  "version": "v1",
  "published": "2018-01-04T23:39:07.000Z",
  "updated": "2018-01-04T23:39:07.000Z",
  "title": "Hitting probabilities and expected hitting times under a weak drift: on the 1/3-rule and beyond",
  "authors": [
    "Peter Pfaffelhuber",
    "Anton Wakolbinger"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR",
    "q-bio.PE"
  ],
  "abstract": "When does a small drift increase the hitting probability of a boundary point / the expected hitting time of the boundary, compared to the driftless case? We analyze this for diffusion processes on [0,1] by expanding the Green function. In this way, in the appropriate diffusion approximation setting, we rederive and extend the one-third rule of evolutionary game theory (Nowak et al., 2004) and effects of stochastic slowdown (Altrock and Traulsen, 2009).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-04T23:39:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J70",
      "91A22",
      "92D15",
      "91A15"
    ],
    "keywords": [
      "expected hitting time",
      "hitting probability",
      "weak drift",
      "small drift increase",
      "evolutionary game theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}