{
  "id": "1810.04691",
  "version": "v1",
  "published": "2018-10-10T18:03:11.000Z",
  "updated": "2018-10-10T18:03:11.000Z",
  "title": "Probabilistic error analysis for some approximation schemes to optimal control problems",
  "authors": [
    "Athena Picarelli",
    "Christoph Reisinger"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We introduce a class of numerical schemes for optimal control problems based on a novel Markov chain approximation, which uses, in turn, a piecewise constant policy approximation, Euler-Maruyama time stepping, and a Gauss-Hermite approximation of the Gaussian increments. We provide lower error bounds of order arbitrarily close to 1/2 in time and 1/3 in space for Lipschitz viscosity solutions, coupling probabilistic arguments with regularization techniques as introduced by Krylov. The corresponding order of the upper bounds is 1/4 in time and 1/5 in space. For sufficiently regular solutions, the order is 1 in both time and space for both bounds. Finally, we propose techniques for further improving the accuracy of the individual components of the approximation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-10T18:03:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control problems",
      "probabilistic error analysis",
      "approximation schemes",
      "novel markov chain approximation",
      "lipschitz viscosity solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}