{
  "id": "1411.7688",
  "version": "v1",
  "published": "2014-11-27T19:35:04.000Z",
  "updated": "2014-11-27T19:35:04.000Z",
  "title": "Absolute Continuity under Time Shift for Ornstein-Uhlenbeck type Processes with Delay or Anticipation",
  "authors": [
    "Jörg-Uwe Löbus"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The paper is concerned with one-dimensional two-sided Ornstein-Uhlenbeck type processes with delay or anticipation. We prove existence and uniqueness requiring almost sure boundedness on the left half-axis in case of delay and almost sure boundedness on the right half-axis in case of anticipation. For those stochastic processes $(X,P_{\\mu})$ we calculate the Radon-Nikodym density under time shift of trajectories, $P_{\\mu}(dX_{\\cdot -t})/P_{\\mu}(dX)$, $t\\in {\\Bbb R}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-27T19:35:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60H10"
    ],
    "keywords": [
      "time shift",
      "absolute continuity",
      "anticipation",
      "sure boundedness",
      "one-dimensional two-sided ornstein-uhlenbeck type processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.7688L"
    }
  }
}