{
  "id": "1404.3367",
  "version": "v2",
  "published": "2014-04-13T11:01:03.000Z",
  "updated": "2016-04-14T06:01:50.000Z",
  "title": "Parisian quasi-stationary distributions for asymmetric Lévy processes",
  "authors": [
    "Irmina Czarna",
    "Zbigniew Palmowski"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In recent years there has been some focus on quasi-stationary behaviour of an one-dimensional L\\'evy process $X$, where we ask for the law $P(X_t\\in dy | \\tau^-_0>t)$ for $t\\to\\infty$ and $\\tau_0^-=\\inf\\{t\\geq 0: X_t<0\\}$. In this paper we address the same question for so-called Parisian ruin time $\\tau^\\theta$, that happens when process stays below zero longer than independent exponential random variable with intensity $\\theta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-13T11:01:03.000Z",
      "abstract": "In recent years there has been some focus on quasi-stationary behaviour of an one-dimensional L\\'evy process, where we ask for the law $P(X_t\\in dy | \\tau^-_0>t)$ for $t\\to\\infty$ and $\\tau_0^-=\\inf\\{t\\geq 0: X_t<0\\}$. In this paper we address the same question for so-called Parisian ruin time $\\tau^\\theta$, that happens when process stays below zero longer than independent exponential random variable with intensity $\\theta$.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-04-14T06:01:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymmetric lévy processes",
      "parisian quasi-stationary distributions",
      "parisian ruin time",
      "one-dimensional levy process",
      "process stays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.3367C"
    }
  }
}