{
  "id": "2104.06385",
  "version": "v1",
  "published": "2021-04-13T17:40:08.000Z",
  "updated": "2021-04-13T17:40:08.000Z",
  "title": "Some examples of solutions to an inverse problem for the first-passage place of a jump-diffusion process",
  "authors": [
    "Mario Abundo"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We report some additional examples of explicit solutions to an inverse first-passage place problem for one-dimensional diffusions with jumps, introduced in a previous paper. If $X(t)$ is a one-dimensional diffusion with jumps, starting from a random position $\\eta \\in [a,b],$ let be $\\tau_{a,b}$ the time at which $X(t)$ first exits the interval $(a,b),$ and $\\pi _a = P(X(\\tau_{a,b}) \\le a)$ the probability of exit from the left of $(a,b).$ Given a probability $q \\in (0,1),$ the problem consists in finding the density $g$ of $\\eta$ (if it exists) such that $\\pi _a = q;$ it can be seen as a problem of optimization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-13T17:40:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60H05",
      "60H10"
    ],
    "keywords": [
      "inverse problem",
      "jump-diffusion process",
      "one-dimensional diffusion",
      "inverse first-passage place problem",
      "explicit solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}