{
  "id": "math/0408178",
  "version": "v2",
  "published": "2004-08-13T10:58:23.000Z",
  "updated": "2004-08-24T11:34:14.000Z",
  "title": "On occupation times of stationary excursions",
  "authors": [
    "Marina Kozlova",
    "Paavo Salminen"
  ],
  "comment": "32 pages; extended abstract",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper excursions of a stationary diffusion in stationary state are studied. In particular, we compute the joint distribution of the occupation times $I^{(+)}_t$ and $I^{(-)}_t$ above and below, respectively, the observed level at time $t$ during an excursion. We consider also the starting time $g_t$ and the ending time $d_t$ of the excursion (straddling $t$) and discuss their relations to the Levy measure of the inverse local time. It is seen that the pairs $(I^{(+)}_t, I^{(-)}_t)$ and $(t-g_t, d_t-t)$ are identically distributed. Moreover, conditionally on $I^{(+)}_t + I^{(-)}_t =v$, the variables $I^{(+)}_t$ and $I^{(-)}_t$ are uniformly distributed on $(0,v)$. Using the theory of the Palm measures, we derive an analoguous result for excursion bridges.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-08-24T11:34:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60G10"
    ],
    "keywords": [
      "occupation times",
      "stationary excursions",
      "inverse local time",
      "stationary diffusion",
      "paper excursions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8178K"
    }
  }
}