{
  "id": "2207.07081",
  "version": "v1",
  "published": "2022-07-14T17:30:24.000Z",
  "updated": "2022-07-14T17:30:24.000Z",
  "title": "Large Deviations for Lévy Diffusions in small regime",
  "authors": [
    "Pedro Catuogno",
    "André de Oliveira Gomes"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1909.10894",
  "categories": [
    "math.PR"
  ],
  "abstract": "This article concerns the large deviations regime and the consequent solution of the Kramers problem for a two-time scale stochastic system driven by a common jump noise signal perturbed in small intensity $\\varepsilon>0$ and with accelerated jumps by intensity $\\frac{1}{\\varepsilon}$. We establish Freidlin-Wentzell estimates for the slow process of the multiscale system in the small noise limit $\\varepsilon \\rightarrow 0$ using the weak convergence approach to large deviations theory. The core of our proof is the reduction of the large deviations principle to the establishment of a stochastic averaging principle for auxiliary controlled processes. As consequence we solve the first exit time/ exit locus problem from a bounded domain containing the stable state of the averaged dynamics for the family of the slow processes in the small noise limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-14T17:30:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviations",
      "small regime",
      "lévy diffusions",
      "small noise limit",
      "two-time scale stochastic system driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}