{
  "id": "1810.10590",
  "version": "v1",
  "published": "2018-10-24T19:50:21.000Z",
  "updated": "2018-10-24T19:50:21.000Z",
  "title": "New insights on concentration inequalities for self-normalized martingales",
  "authors": [
    "Bernard Bercu",
    "Taieb Touati"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more flexibility and allows us to improve previous concentration inequalities. Statistical applications on autoregressive process, internal diffusion-limited aggregation process, and online statistical learning are also provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-24T19:50:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60G42",
      "60G15",
      "60J80"
    ],
    "keywords": [
      "concentration inequalities",
      "self-normalized martingales",
      "internal diffusion-limited aggregation process",
      "total quadratic variation",
      "predictable quadratic variation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}