{
  "abstract": "In this paper, we provide sufficient conditions for the absolute continuity of one-dimensional push-forwards of dependent random vectors. Suppose that $X$ has an absolutely continuous distribution and that the conditional distribution of an $\\mathbb{R}^d$-valued random vector $Y$ given $X=x$ is nondecreasing in $x\\in \\mathbb{R}$ in the usual stochastic order. For Borel maps $g\\colon \\mathbb{R}\\times\\mathbb{R}^d\\to\\mathbb{R}$ satisfying a coordinatewise monotonicity condition in $Y$ and a uniform lower-increment condition in $X$, we prove that $g(X,Y)$ has an absolutely continuous distribution. The result requires neither independence nor a joint density, and allows the marginal law of $Y$ to be completely arbitrary. Moreover, the result remains valid if $\\mathbb{R}^d$ is replaced by an arbitrary measurable space endowed with a reflexive binary relation. We discuss consequences for monotone risk aggregation and extensions of the familiar regularization by convolution beyond independent random variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.21042",
  "author_total": 2,
  "authors": [
    {
      "name": "Ben Goldys"
    },
    {
      "name": "Max Nendel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dzb36wg9c6c57.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.21042",
  "fulltext_url": null,
  "id": "dzb36wg9c6c57",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.21042",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-fin.RM"
    ],
    [
      "openalex",
      "1803|Probability and Risk Models"
    ]
  ],
  "openalex": "W7165668617",
  "pdf_url": "https://arxiv.org/pdf/2606.21042",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dzb36wg9c6c57.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2606.21042",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.21042"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Absolute Continuity of Monotone Aggregations under Positive Regression Dependence",
  "title_text": "Absolute Continuity of Monotone Aggregations under Positive Regression Dependence",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/dzb36wg9c6c57",
  "venue": "arXiv",
  "versions": []
}