{
  "id": "2205.04789",
  "version": "v1",
  "published": "2022-05-10T10:32:21.000Z",
  "updated": "2022-05-10T10:32:21.000Z",
  "title": "Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension",
  "authors": [
    "Florian Bechtold"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a regularization by noise phenomenon for the continuous parabolic Anderson model with a potential shifted along paths of fractional Brownian motion. We demonstrate that provided the Hurst parameter is chosen sufficiently small, this shift allows to establish well-posedness and stability to the corresponding problem - without the need of renormalization - in any dimension. We moreover provide a robustified Feynman-Kac type formula for the unique solution to the regularized problem building upon regularity estimates for the local time of fractional Brownian motion as well as non-linear Young integration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-10T10:32:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary dimension",
      "random translation",
      "continuous pam",
      "related models",
      "fractional brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}