{
  "id": "1105.1435",
  "version": "v1",
  "published": "2011-05-07T11:57:51.000Z",
  "updated": "2011-05-07T11:57:51.000Z",
  "title": "Levy targeting and the principle of detailed balance",
  "authors": [
    "Piotr Garbaczewski",
    "Vladimir Stephanovich"
  ],
  "journal": "Phys. Rev. E 84, (2011), 011109",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We investigate confined L\\'{e}vy flights under premises of the principle of detailed balance. The master equation admits a transformation to L\\'{e}vy - Schr\\\"{o}dinger semigroup dynamics (akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation). We solve a stochastic targeting problem for arbitrary stability index $0<\\mu <2$ of L\\'{e}vy drivers: given an invariant probability density function (pdf), specify the jump - type dynamics for which this pdf is a long-time asymptotic target. Our (\"$\\mu$-targeting\") method is exemplified by Cauchy family and Gaussian target pdfs. We solve the reverse engineering problem for so-called L\\'{e}vy oscillators: given a quadratic semigroup potential, find an asymptotic pdf for the associated master equation for arbitrary $\\mu$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-07T11:57:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.40.Jc",
      "02.50.Ey",
      "05.20.-y",
      "05.10.Gg"
    ],
    "keywords": [
      "detailed balance",
      "levy targeting",
      "invariant probability density function",
      "master equation admits",
      "arbitrary stability index"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "doi": "10.1103/PhysRevE.84.011142",
      "year": 2011,
      "month": "Jul",
      "volume": 84,
      "number": 1,
      "pages": "011142"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvE..84a1142G"
    }
  }
}