{
  "id": "math/0702541",
  "version": "v1",
  "published": "2007-02-19T13:33:26.000Z",
  "updated": "2007-02-19T13:33:26.000Z",
  "title": "First hitting time and place, monopoles and multipoles for pseudo-processes driven by the equation $\\partial/\\partial t = \\pm\\partial^N/\\partial x^N$",
  "authors": [
    "Aimé Lachal"
  ],
  "comment": "51 pages",
  "journal": "Electronical Journal of Probability, vol. 12 (2007), pp. 300-353",
  "doi": "10.1214/EJP.v12-399",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider the high-order heat-type equation $\\partial u/\\partial t=\\pm\\partial^N u/\\partial x^N$ for an integer $N>2$ and introduce the related Markov pseudo-process $(X(t))_{t\\ge 0}$. In this paper, we study several functionals related to $(X(t))_{t\\ge 0}$: the maximum $M(t)$ and minimum $m(t)$ up to time $t$; the hitting times $\\tau_a^+$ and $\\tau_a^-$ of the half lines $(a,+\\infty)$ and $(-\\infty,a)$ respectively. We provide explicit expressions for the distributions of the vectors $(X(t),M(t))$ and $(X(t),m(t))$, as well as those of the vectors $(\\tau_a^+,X(\\tau_a^+))$ and $(\\tau_a^-,X(\\tau_a^-))$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-19T13:33:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G20",
      "60J25"
    ],
    "keywords": [
      "first hitting time",
      "pseudo-processes driven",
      "multipoles",
      "high-order heat-type equation",
      "half lines"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}