{
  "annotation_id": "747a8ebd-98f9-43aa-ad12-5c816a51c805",
  "date_created": "2026-02-17T05:53:20.216000Z",
  "date_modified": "2026-02-17T05:53:20.216000Z",
  "file_hash": "d8525d43e919d0fb4ab167aeec93eb280b6f5fd717c6c92af48c9022823d6e0a",
  "private": false,
  "record": {
    "abstract": "In this paper we extend the notion of $\\varphi$-mixing to set-valued random sequences that take values in the family of closed subsets of a Banach space. Several strong laws of large numbers for such $\\varphi$-mixing sequences are stated and proved. Illustrative examples show that the hypotheses of the theorems are both natural and sharp.",
    "arxiv_id": "2601.09197",
    "authors": [
      "Luc Tri Tuyen"
    ],
    "categories": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On strong law of large numbers for weakly stationary $\\varphi$-mixing set-valued random variable sequences",
    "url": "https://arxiv.org/abs/2601.09197",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e432c0ed-46ec-410f-9b0b-37c31d79cda1",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}