{
  "id": "2406.15801",
  "version": "v1",
  "published": "2024-06-22T10:01:23.000Z",
  "updated": "2024-06-22T10:01:23.000Z",
  "title": "Limit theorems for Gaussian fields via Chaos Expansions and Applications",
  "authors": [
    "Giacomo Giorgio"
  ],
  "comment": "PhD thesis",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this PhD thesis, we apply a combination of Malliavin calculus and Stein's method in the framework of probability approximations. The specific problems we tackle with these methods are motivated by probabilistic models in cosmology (Part I: Quantitative CLTs for non linear functionals of random hyperspherical harmonics) and finance (Part II: The fractional Ornstein-Uhlenbeck process in rough volatility modelling). In this second part we also apply techniques from Large Deviations theory (Section: Short-time asymptotics for non self-similar stochastic volatility models).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-22T10:01:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian fields",
      "chaos expansions",
      "limit theorems",
      "non self-similar stochastic volatility models",
      "applications"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}