{
  "id": "1106.3893",
  "version": "v1",
  "published": "2011-06-20T13:23:07.000Z",
  "updated": "2011-06-20T13:23:07.000Z",
  "title": "Anomalous diffusion for a correlated process with long jumps",
  "authors": [
    "Tomasz Srokowski"
  ],
  "comment": "10 pages, 6 figures",
  "journal": "Physica A 390 (2011) 3077--3085",
  "doi": "10.1016/j.physa.2011.04.022",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\\'evy distribution; it is assumed as a jumping process (the kangaroo process) with a variable jumping rate. Both the exponential and the algebraic form of the covariance -- defined for the truncated distribution -- are considered. It is demonstrated by numerical calculations that the stationary solution of the master equation for the case of power-law correlations decays with time, but a simple modification of the process makes the tails stable. The main result of the paper is a finding that -- in contrast to the velocity fluctuations -- the position variance may be finite. It rises with time faster than linearly: the diffusion is anomalously enhanced. On the other hand, a process which follows from a superposition of the Ornstein-Uhlenbeck-L\\'evy processes always leads to position distributions with a divergent variance which means accelerated diffusion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-20T13:23:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long jumps",
      "correlated process",
      "anomalous diffusion",
      "power-law correlations decays",
      "algebraic form"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Physica A Statistical Mechanics and its Applications",
      "year": 2011,
      "month": "Sep",
      "volume": 390,
      "number": "18-19",
      "pages": 3077
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhyA..390.3077S"
    }
  }
}