{
  "id": "2204.01419",
  "version": "v1",
  "published": "2022-04-04T12:12:40.000Z",
  "updated": "2022-04-04T12:12:40.000Z",
  "title": "Stability of estimates for fundamental solutions under Feynman-Kac perturbations for symmetric Markov processes",
  "authors": [
    "Daehong Kim",
    "Panki Kim",
    "Kazuhiro Kuwae"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "In this paper, when a given symmetric Markov process X satisfies the stability of global heat kernel two-sided (upper) estimates by Markov perturbations, we give a necessary and sufficient condition on the stability of global two-sided (upper) estimates for fundamental solution of Feynman-Kac semigroup of X. As a corollary, under the same assumptions, a weak type global two-sided (upper) estimates holds for the fundamental solution of Feynman-Kac semigroup with (extended) Kato class conditions for measures. This generalizes all known results on the stability of global integral kernel estimates by symmetric Feynman-Kac perturbations with Kato class conditions in the framework of symmetric Markov processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-04T12:12:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C25",
      "60J45",
      "60J46",
      "60J57",
      "35J10",
      "60J35",
      "60J25",
      "60J76"
    ],
    "keywords": [
      "symmetric markov process",
      "fundamental solution",
      "kato class conditions",
      "global integral kernel estimates",
      "feynman-kac semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}