{
  "abstract": "In the present paper, we consider a $d$-dimensional time-homogeneous stochastic differential equation with diffusion matrix $a$ and no drift coefficient. We check that the convexity in the starting position $x$ of the distribution of its solution on the path space when the codomain is endowed with the convex order is equivalent to the convexity of $\\R^d\\ni x\\mapsto \\sqrt{ζ^*a(x)ζ}$ for each $ζ\\in\\R^d$. To do so, we introduce the seemingly stronger notion of coupling-convexity in the starting position and check that it is also equivalent to the convexity of the above square-rooted functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11528",
  "author_total": 1,
  "authors": [
    {
      "name": "Benjamin Jourdain"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4arc6rqykg5c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11528",
  "fulltext_url": null,
  "id": "d4arc6rqykg5c",
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  "landing_url": "https://hal.science/hal-05788093v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
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      "hal",
      "0.math"
    ],
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      "openalex",
      "2003|Stochastic processes and financial applications"
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  "openalex": "W7221196441",
  "pdf_url": "https://arxiv.org/pdf/2610.11528",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4arc6rqykg5c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:52Z",
      "native_id": "hal-05788093",
      "source": "hal",
      "url": "https://hal.science/hal-05788093v1"
    },
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11528",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11528"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Coupling-convexity of a diffusion with respect to its starting position",
  "title_text": "Coupling-convexity of a diffusion with respect to its starting position",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/d4arc6rqykg5c",
  "venue": "HAL",
  "versions": []
}