{
  "id": "2303.08788",
  "version": "v1",
  "published": "2023-03-15T17:30:47.000Z",
  "updated": "2023-03-15T17:30:47.000Z",
  "title": "Asymptotic results for compound sums in Banach Spaces",
  "authors": [
    "Claudio Macci",
    "Barbara Pacchiarotti"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove large and moderate deviation results for sequences of compound sums, where the summands are i.i.d. random variables taking values on a Banach space. We establish that the results hold by proving that we are dealing with exponentially tight sequences. We present two moderate deviation results: in the first one the summands are centered, in the second one the compound sums are centered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-15T17:30:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G50",
      "60B12"
    ],
    "keywords": [
      "compound sums",
      "banach space",
      "asymptotic results",
      "moderate deviation results",
      "exponentially tight sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}