{
  "id": "1111.4159",
  "version": "v3",
  "published": "2011-11-17T17:22:59.000Z",
  "updated": "2013-01-10T16:33:46.000Z",
  "title": "Power and exponential moments of the number of visits and related quantities for perturbed random walks",
  "authors": [
    "Gerold Alsmeyer",
    "Alexander Iksanov",
    "Matthias Meiners"
  ],
  "comment": "38 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $(\\xi_1,\\eta_1),(\\xi_2,\\eta_2),...$ be a sequence of i.i.d.\\ copies of a random vector $(\\xi,\\eta)$ taking values in $\\R^2$, and let $S_n := \\xi_1+...+\\xi_n$. The sequence $(S_{n-1} + \\eta_n)_{n \\geq 1}$ is then called perturbed random walk. We study random quantities defined in terms of the perturbed random walk: $\\tau(x)$, the first time the perturbed random walk exits the interval $(-\\infty,x]$, $N(x)$, the number of visits to the interval $(-\\infty,x]$, and $\\rho(x)$, the last time the perturbed random walk visits the interval $(-\\infty,x]$. We provide criteria for the a.s.\\ finiteness and for the finiteness of exponential moments of these quantities. Further, we provide criteria for the finiteness of power moments of $N(x)$ and $\\rho(x)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-01-10T16:33:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60G40"
    ],
    "keywords": [
      "exponential moments",
      "related quantities",
      "perturbed random walk visits",
      "perturbed random walk exits",
      "finiteness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.4159A"
    }
  }
}