{
  "id": "1205.2941",
  "version": "v2",
  "published": "2012-05-14T05:24:31.000Z",
  "updated": "2015-10-27T06:34:01.000Z",
  "title": "Boundary crossing probabilities for diffusions with piecewise linear drifts",
  "authors": [
    "Jinghai Shao",
    "Liqun Wang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of the Laplace transforms of the first passage densities for diffusions with piecewise linear drifts. The proposed method is applied to a reliability problem where the standard degradation model based on Wiener process is extended to diffusion processes with piecewise linear drifts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-14T05:24:31.000Z",
      "abstract": "In this work we study boundary crossing probabilities of general one-dimensional diffusion processes with respect to constant boundaries. We first give an explicit formula of the probabilities for diffusions with piecewise linear drift and constant diffusion coefficient in terms of its Laplace transform. Then we provide an approximation scheme to obtain the boundary crossing probabilities for more general diffusions. Finally, an estimate of convergence rate of the approximation is also given.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-10-27T06:34:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60J75",
      "60J60",
      "60J70"
    ],
    "keywords": [
      "piecewise linear drift",
      "general one-dimensional diffusion processes",
      "study boundary crossing probabilities",
      "constant diffusion coefficient",
      "approximation scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.2941S"
    }
  }
}