{
  "id": "math/0602385",
  "version": "v1",
  "published": "2006-02-17T17:13:08.000Z",
  "updated": "2006-02-17T17:13:08.000Z",
  "title": "Discretisation of stochastic control problems for continuous time dynamics with delay",
  "authors": [
    "Markus Fischer",
    "Markus Reiss"
  ],
  "comment": "submitted to JCAM",
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow for delay in the dynamics. The existence of an optimal strategy with respect to the cost functional can be guaranteed in the class of relaxed controls. Weak convergence of the approximating extended Markov chains to the original process together with convergence of the associated optimal strategies is established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-17T17:13:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20"
    ],
    "keywords": [
      "stochastic control problems",
      "continuous time dynamics",
      "discretisation",
      "optimal strategy",
      "approximating extended markov chains"
    ],
    "publication": {
      "journal": "Journal of Computational and Applied Mathematics",
      "year": 2007,
      "month": "Aug",
      "volume": 205,
      "number": 2,
      "pages": 969
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007JCoAM.205..969F"
    }
  }
}