{
  "id": "0907.0762",
  "version": "v1",
  "published": "2009-07-04T14:05:17.000Z",
  "updated": "2009-07-04T14:05:17.000Z",
  "title": "Poincaré inequality and exponential integrability of hitting times for linear diffusions",
  "authors": [
    "D. Loukianova",
    "O. Loukianov",
    "Sh. Song"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $X$ be a regular linear continuous positively recurrent Markov process with state space $\\R$, scale function $S$ and speed measure $m$. For $a\\in \\R$ denote B^+_a&=\\sup_{x\\geq a} \\m(]x,+\\infty[)(S(x)-S(a)) B^-_a&=\\sup_{x\\leq a} \\m(]-\\infty;x[)(S(a)-S(x)) We study some characteristic relations between $B^+_a$, $B^-_a$, the exponential moments of the hitting times $T_a$ of $X$, the Hardy and Poincar\\'e inequalities for the Dirichlet form associated with $X$. As a corollary, we establish the equivalence between the existence of exponential moments of the hitting times and the spectral gap of the generator of $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-04T14:05:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60J35",
      "60J60"
    ],
    "keywords": [
      "hitting times",
      "linear diffusions",
      "exponential integrability",
      "inequality",
      "exponential moments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.0762L"
    }
  }
}