{
  "id": "2007.06484",
  "version": "v1",
  "published": "2020-07-13T16:35:28.000Z",
  "updated": "2020-07-13T16:35:28.000Z",
  "title": "The continuum directed polymer in Lévy Noise",
  "authors": [
    "Quentin Berger",
    "Hubert Lacoin"
  ],
  "comment": "55 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present in this paper the construction of a continuum directed polymer model in an environment given by space-time L\\'evy noise. One of the main objectives of this construction is to describe the scaling limit of discrete directed polymer in an heavy-tail environment and for this reason we put special emphasis on the case of $\\alpha$-stable noises with $\\alpha \\in (1,2)$. Our construction can be performed in arbitrary dimension, provided that the L\\'evy measure satisfies specific (and dimension dependent) conditions. We also discuss a few basic properties of the continuum polymer and the relation between this model and the Stochastic Heat Equation with multiplicative L\\'evy noise.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-13T16:35:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G57",
      "82B44",
      "60H15"
    ],
    "keywords": [
      "lévy noise",
      "levy measure satisfies specific",
      "space-time levy noise",
      "construction",
      "continuum directed polymer model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}