{
  "id": "2402.13748",
  "version": "v2",
  "published": "2024-02-21T12:18:27.000Z",
  "updated": "2024-09-04T08:46:59.000Z",
  "title": "Nonlinear effects within invariance principles",
  "authors": [
    "Maximilian Engel",
    "Peter K. Friz",
    "Tal Orenshtein"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The combination of functional limit theorems with the pathwise analysis of deterministic and stochastic differential equations has proven to be a powerful approach to the analysis of fast-slow systems. In a multivariate setting, this requires rough path ideas, as already suggested in the seminal work [Melbourne-Stuart, Nonlinearity, 24, 2011]. This initiated a program pursued by numerous authors and which has required substantial results on invariance principles (also known as functional central limit theorems) in rough path topologies. We take a unified point of view and provide simple and exact formulas, of the Green-Kubo type, that characterize the relevant Brownian rough path limits and discuss how they naturally apply in different settings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-09-04T08:46:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariance principles",
      "nonlinear effects",
      "relevant brownian rough path limits",
      "functional central limit theorems",
      "stochastic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}