{
  "id": "1509.08138",
  "version": "v1",
  "published": "2015-09-27T20:43:23.000Z",
  "updated": "2015-09-27T20:43:23.000Z",
  "title": "On the strong approximations of partial sums of f(nkx)",
  "authors": [
    "Marko Raseta"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove a strong invariance principle for the sums PN k=1 f(nkx), where f is a smooth periodic function on R and (nk)k?1 is an increasing random sequence. Our results show that in contrast to the classical Salem-Zygmund theory, the asymptotic properties of lacunary series with random gaps can be described very precisely without any assumption on the size of the gaps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-27T20:43:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partial sums",
      "strong approximations",
      "strong invariance principle",
      "smooth periodic function",
      "sums pn"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150908138R"
    }
  }
}