{
  "id": "2107.10774",
  "version": "v1",
  "published": "2021-07-22T16:03:22.000Z",
  "updated": "2021-07-22T16:03:22.000Z",
  "title": "Tempered fractional Brownian motion on finite intervals",
  "authors": [
    "Thomas Vojta",
    "Zachary Miller",
    "Samuel Halladay"
  ],
  "comment": "11 pages, 13 figures included",
  "categories": [
    "cond-mat.stat-mech",
    "physics.bio-ph"
  ],
  "abstract": "Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic correlation time the power-law correlations between the increments of fractional Brownian motion. Here, we investigate such tempered fractional Brownian motion confined to a finite interval by reflecting walls. Specifically, we explore how the tempering of the long-time correlations affects the strong accumulation and depletion of particles near reflecting boundaries recently discovered for untempered fractional Brownian motion. We find that exponential tempering introduces a characteristic size for the accumulation and depletion zones but does not affect the functional form of the probability density close to the wall. In contrast, power-law tempering leads to more complex behavior that differs between the superdiffusive and subdiffusive cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-22T16:03:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite interval",
      "probability density close",
      "complex systems features",
      "long-time correlations affects",
      "untempered fractional brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}