{
  "id": "1808.01667",
  "version": "v1",
  "published": "2018-08-05T18:30:25.000Z",
  "updated": "2018-08-05T18:30:25.000Z",
  "title": "Homogenization of Symmetric Lévy Processes on $\\mathbb{R}^d$",
  "authors": [
    "René L. Schilling",
    "Toshihiro Uemura"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this short note we study homogenization of symmetric $d$-dimensional L\\'evy processes. Homogenization of one-dimensional pure jump Markov processes has been investigated by Tanaka \\emph{et al.} in 1992; their motivation was the work by Benssousan \\emph{et al.}\\ from 1975 on the homogenization of diffusion processes in $\\mathbb{R}^d$. We investigate a similar problem for a class of symmetric pure-jump L\\'evy processes on $\\mathbb{R}^d$ and we identify -- using Mosco convergence -- the limit process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-05T18:30:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric lévy processes",
      "one-dimensional pure jump markov processes",
      "symmetric pure-jump levy processes",
      "dimensional levy processes",
      "study homogenization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}