{
  "id": "1909.07213",
  "version": "v1",
  "published": "2019-09-13T11:54:07.000Z",
  "updated": "2019-09-13T11:54:07.000Z",
  "title": "Continuous time random walks and Lévy walks with stochastic resetting",
  "authors": [
    "Tian Zhou",
    "Pengbo Xu",
    "Weihua Deng"
  ],
  "comment": "9 pages, 5 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and L\\'{e}vy walk, in which the particles are stochastically reset to a given position with a resetting rate $r$. The mean squared displacements of the CTRW and L\\'{e}vy walks with stochastic resetting are calculated, uncovering that the stochastic resetting always makes the CTRW process localized and L\\'{e}vy walk diffuse slower. The asymptotic behaviors of the probability density function of L\\'evy walk with stochastic resetting are carefully analyzed under different scales of $x$, and a striking influence of stochastic resetting is observed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-13T11:54:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic resetting",
      "lévy walks",
      "intermittent stochastic processes appear",
      "intermittent continuous time random walk",
      "walk diffuse slower"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}