{
  "id": "2109.01027",
  "version": "v1",
  "published": "2021-09-02T15:45:09.000Z",
  "updated": "2021-09-02T15:45:09.000Z",
  "title": "Hölder regularity for stochastic processes with bounded and measurable increments",
  "authors": [
    "Ángel Arroyo",
    "Pablo Blanc",
    "Mikko Parviainen"
  ],
  "comment": "39 pages",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We obtain an asymptotic H\\\"older estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, is a counterpart to the Krylov-Safonov regularity result in PDEs. However, the discrete step size $\\varepsilon$ has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-02T15:45:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J15",
      "60H30",
      "60J10",
      "91A50"
    ],
    "keywords": [
      "hölder regularity",
      "measurable increments",
      "krylov-safonov regularity result",
      "discrete extremal operators",
      "functions satisfying pucci-type inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}