{
  "id": "1011.3379",
  "version": "v2",
  "published": "2010-11-15T13:42:43.000Z",
  "updated": "2011-01-13T11:46:42.000Z",
  "title": "Time Reversal of Some Stationary Jump-Diffusion Processes from Population Genetics",
  "authors": [
    "Martin Hutzenthaler",
    "Jesse E. Taylor"
  ],
  "comment": "23 pages, 1 figure, Advances in Applied Probability Vol 42, No 4, p 1147-1171, 2010",
  "categories": [
    "math.PR"
  ],
  "abstract": "We describe the processes obtained by time reversal of a class of stationary jump-diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion, then time reversal leads to a jump-diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible, then the jumps off of that point are governed by a weighted local time of the time-reversed process.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-13T11:46:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J55",
      "92D10"
    ],
    "keywords": [
      "stationary jump-diffusion processes",
      "time reversal",
      "population genetics",
      "boundary point",
      "forward process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.3379H"
    }
  }
}