{
  "id": "2401.06248",
  "version": "v1",
  "published": "2024-01-11T20:26:41.000Z",
  "updated": "2024-01-11T20:26:41.000Z",
  "title": "Simulating diffusion bridges using the Wiener chaos expansion",
  "authors": [
    "Francisco Delgado-Vences",
    "Gabriel Adrián Salcedo-Varela",
    "Fernando Baltazar-Larios"
  ],
  "comment": "21 pages, 5 figures, 1 algorithm",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we simulate diffusion bridges by using an approximation of the Wiener-chaos expansion (WCE), or a Fourier-Hermite expansion, for a related diffusion process. Indeed, we consider the solution of stochastic differential equations, and we apply the WCE to a particular representation of the diffusion bridge. Thus, we obtain a method to simulate the proposal diffusion bridges that is fast and that in every attempt constructs a diffusion bridge, which means there are no rejection rates. The method presented in this work could be very useful in statistical inference. We validate the method with a simple Ornstein-Uhlenbeck process. We apply our method to three examples of SDEs and show the numerical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-11T20:26:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60Gxx"
    ],
    "keywords": [
      "wiener chaos expansion",
      "simulating diffusion bridges",
      "stochastic differential equations",
      "simulate diffusion bridges",
      "simple ornstein-uhlenbeck process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}