{
  "id": "2208.00674",
  "version": "v1",
  "published": "2022-08-01T08:10:06.000Z",
  "updated": "2022-08-01T08:10:06.000Z",
  "title": "A fixed-point theorem for local operators with applications to stochastic equations",
  "authors": [
    "Arcady Ponosov"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fixed-point theorem for compact operators. The illustrative examples explain how this analysis can be applied to stochastic differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-01T08:10:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H10",
      "46N30"
    ],
    "keywords": [
      "stochastic equations",
      "local operators",
      "applications",
      "nonlinear non-compact operator equations",
      "schauders fixed-point theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}