{
  "abstract": "In this paper, we consider the quasi-copulas and copulas with a prescribed sub-track section, i.e., with given values along the curve segment connecting the points (x0,0) and (1,1-x0) for 0<x0<1. By employing the technique based on the W-ordinal sum, we provide methods for constructing quasi-copulas and copulas whose sub-track section coincides with a given one. Then, we further investigate construction methods for symmetric quasi-copulas and copulas with a prescribed sub-track section. Furthermore, we determine the best-possible bounds for the class of quasi-copulas sharing a common sub-track section, and verify that the lower bound obtained is also the best-possible lower bound for the class of copulas with a common sub-track section. Finally, we examine several properties of the bound (quasi-)copulas with a prescribed sub-track section, including their comparison with bound (quasi-)copulas with a given track section or a sub-diagonal section, as well as their statistical characteristic and concordance order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01247",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiehua Xie"
    },
    {
      "name": "Wei Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/094t8sch5caj8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01247",
  "fulltext_url": null,
  "id": "094t8sch5caj8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01247",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Financial Risk and Volatility Modeling"
    ]
  ],
  "openalex": "W7215715696",
  "pdf_url": "https://arxiv.org/pdf/2610.01247",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/094t8sch5caj8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01247",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01247"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Quasi-copulas with a prescribed sub-track section",
  "title_text": "Quasi-copulas with a prescribed sub-track section",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/094t8sch5caj8",
  "venue": "arXiv",
  "versions": []
}