{
  "id": "0809.0813",
  "version": "v2",
  "published": "2008-09-04T13:48:07.000Z",
  "updated": "2023-01-30T17:20:23.000Z",
  "title": "Large Deviations of Vector-valued Martingales in 2-Smooth Normed Spaces",
  "authors": [
    "Anatoli Juditsky",
    "Arkadii S. Nemirovski"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We derive exponential bounds on probabilities of large deviations for \"light tail\" martingales taking values in finite-dimensional normed spaces. Our primary emphasis is on the case where the bounds are dimension-independent or nearly so. We demonstrate that this is the case when the norm on the space can be approximated, within an absolute constant factor, by a norm which is differentiable on the unit sphere with a Lipschitz continuous gradient. We also present various examples of spaces possessing the latter property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-04T13:48:07.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2023-01-30T17:20:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviations",
      "vector-valued martingales",
      "absolute constant factor",
      "light tail",
      "primary emphasis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.0813J"
    }
  }
}