{
  "id": "1712.04098",
  "version": "v1",
  "published": "2017-12-12T02:05:45.000Z",
  "updated": "2017-12-12T02:05:45.000Z",
  "title": "Normal Convergence Using Malliavin Calculus With Applications and Examples",
  "authors": [
    "Juan Jose Viquez R"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1104.1837",
  "journal": "Stochastic Analysis and Applications 2017",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove the chain rule in the more general framework of the Wiener-Poisson space, allowing us to obtain the so-called Nourdin-Peccati bound. From this bound we obtain a second-order Poincare-type inequality that is useful in terms of computations. For completeness we survey these results on the Wiener space, the Poisson space, and the Wiener-Poisson space. We also give several applications to central limit theorems with relevant examples: linear functionals of Gaussian subordinated fields (where the subordinated field can be processes like fractional Brownian motion or the solution of the Ornstein-Uhlenbeck SDE driven by fractional Brownian motion), Poisson functionals in the first Poisson chaos restricted to infinitely many \\small\" jumps (particularly fractional Levy processes) and the product of two Ornstein-Uhlenbeck processes (one in the Wiener space and the other in the Poisson space). We also obtain bounds for their rate of convergence to normality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-12T02:05:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60G15",
      "60G20"
    ],
    "keywords": [
      "malliavin calculus",
      "normal convergence",
      "fractional brownian motion",
      "applications",
      "wiener-poisson space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}