{
  "id": "1207.2719",
  "version": "v3",
  "published": "2012-07-11T17:44:03.000Z",
  "updated": "2018-12-18T18:22:01.000Z",
  "title": "Minimising the expected commute time",
  "authors": [
    "Saul Jacka",
    "Ma. Elena Hernandez-Hernandez"
  ],
  "comment": "21 pages; significant revision; title change; additional author",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "Motivated in part by a problem in simulated tempering (a form of Markov chain Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin to $1$ and then return (the so-called commute time from 0 to 1). We consider the static and dynamic versions of this problem where the control mechanism is related to the diffusion\\rq{}s drift via the corresponding scale function. In the static version the diffusion's drift can be chosen at each point in [0,1], whereas in the dynamic version, we are only able to choose the drift at each point at the time of first visiting that point. The dynamic version leads to a novel type of stochastic control problem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-09T12:21:26.000Z",
      "title": "Minimising the time to reach a target and return",
      "abstract": "Motivated by a problem in simulated tempering (a form of Markov chain Monte Carlo), we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin to 1 and then return. The control mechanism is that we are allowed to chose the diffusion's drift at each point in [0,1]. We consider the static and dynamic versions of this problem, where, in the dynamic version, we are only able to choose the drift at each point at the time of first visiting that point.",
      "comment": "20 pages; minor revision",
      "journal": null,
      "doi": null,
      "authors": [
        "Saul Jacka"
      ]
    },
    {
      "version": "v3",
      "updated": "2018-12-18T18:22:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60J27",
      "60J60",
      "93E20"
    ],
    "keywords": [
      "markov chain monte carlo",
      "dynamic version",
      "minimising",
      "control mechanism",
      "diffusions drift"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2719J"
    }
  }
}