{
  "id": "0708.3562",
  "version": "v1",
  "published": "2007-08-27T09:30:46.000Z",
  "updated": "2007-08-27T09:30:46.000Z",
  "title": "First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes",
  "authors": [
    "A. N. Downes",
    "K. Borovkov"
  ],
  "comment": "27 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original boundary by a different one. In doing so we establish the existence of the first-passage time density and provide an upper bound for this function. In the case of processes with diffusion interval equal to whole real line this is extended to a lower bound, as well as bounds for the first crossing time of a lower boundary. An extension to some time-inhomogeneous diffusions is given. These results are illustrated by numerical examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-27T09:30:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J70"
    ],
    "keywords": [
      "boundary crossing probability",
      "first passage densities",
      "diffusion processes",
      "general curvilinear boundaries",
      "first-passage time density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.3562D"
    }
  }
}