{
  "id": "1603.02506",
  "version": "v1",
  "published": "2016-03-08T12:57:47.000Z",
  "updated": "2016-03-08T12:57:47.000Z",
  "title": "Joint law of the hitting time, overshoot and undershoot for a Lévy process",
  "authors": [
    "Laure Coutin",
    "Waly Ngom"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let be $(X_t, t\\geq 0)$ be a L\\'evy process which is the sum of a Brownian motion with drift and a compound Poisson process. We consider the first passage time $\\tau_x$ at a fixed level $x>0$ by $(X_t, t\\geq 0)$ and $K_x:= X_{\\tau_x}-x$ the overshoot and $L_x:= x-X_{\\tau_x^-}$ the undershoot. We first study the regularity of the density of the first passage time. Secondly, we calculate the joint law of $(\\tau_x, K_x, L_x).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-08T12:57:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "joint law",
      "lévy process",
      "hitting time",
      "first passage time",
      "undershoot"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160302506C"
    }
  }
}