{
  "id": "1207.3758",
  "version": "v2",
  "published": "2012-07-16T18:38:45.000Z",
  "updated": "2014-09-03T11:43:27.000Z",
  "title": "On regularity properties and approximations of value functions for stochastic differential games in domains",
  "authors": [
    "N. V. Krylov"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/13-AOP848 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2014, Vol. 42, No. 5, 2161-2196",
  "doi": "10.1214/13-AOP848",
  "categories": [
    "math.OC"
  ],
  "abstract": "We prove that for any constant $K\\geq1$, the value functions for time homogeneous stochastic differential games in the whole space can be approximated up to a constant over $K$ by value functions whose second-order derivatives are bounded by a constant times $K$. On the way of proving this result we prove that the value functions for stochastic differential games in domains and in the whole space admit estimates of their Lipschitz constants in a variety of settings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-16T18:38:45.000Z",
      "abstract": "We prove that for any constant $K\\geq1$, value functions for time homogeneous stochastic differential games in the whole space can be approximated up to a constant over $K$ by value functions whose second order derivatives are bounded by a constant times $K$. On the way of proving this result we prove that the value functions for stochastic differential games in domains and in the whole space admit estimates of their Lipschitz constants in a variety of settings.",
      "comment": "30 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-03T11:43:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "49N70",
      "91A15"
    ],
    "keywords": [
      "value functions",
      "regularity properties",
      "approximations",
      "time homogeneous stochastic differential games",
      "second order derivatives"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.3758K"
    }
  }
}