{
  "id": "2001.02487",
  "version": "v1",
  "published": "2020-01-08T13:03:37.000Z",
  "updated": "2020-01-08T13:03:37.000Z",
  "title": "Probability distributions for the run-and-tumble models with variable speed and tumbling rate",
  "authors": [
    "Luca Angelani",
    "Roberto Garra"
  ],
  "comment": "Published at https://doi.org/10.15559/18-VMSTA127 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)",
  "journal": "Modern Stochastics: Theory and Applications 2019, Vol. 6, No. 1, 3-12",
  "doi": "10.15559/18-VMSTA127",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed according to a non-stationary Poisson distribution with rate $\\lambda(t)$. We show that, under suitable assumptions, we are able to find the exact form of the probability distribution. We also consider the space-fractional counterpart of this model, finding the characteristic function of the related process. A conclusive discussion is devoted to the potential applications to run-and-tumble models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-08T13:03:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability distribution",
      "run-and-tumble models",
      "tumbling rate",
      "non-stationary poisson distribution",
      "persistent random walk"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}