{
  "abstract": "We study the first passage of Brownian motion to a monomial moving boundary. For every integer degree at least two, we construct a time-independent signed image measure whose heat potential is the killed Brownian transition density on a nonzero interval of the natural Brownian time scale. The image density is determined by a second-kind Volterra equation in the image coordinate, not by the classical Volterra equations in time for the hitting density. Its kernel is an explicit Wright function, and the first-passage density is recovered afterwards from the boundary flux. Exponential bounds establish convergence, while a beta-moment transform connects the Wright kernel with the finite-order differential hierarchy previously obtained from transported moving zeros. A cubic numerical experiment independently checks the resulting density against simulated Brownian paths.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30298",
  "author_total": 1,
  "authors": [
    {
      "name": "Gerardo Hernández-del-Valle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2jc77fbp8ybcd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30298",
  "fulltext_url": null,
  "id": "2jc77fbp8ybcd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30298",
  "language": null,
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.30298",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2jc77fbp8ybcd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30298",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30298"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Generalized Images for Brownian First Passage to Monomial Boundaries",
  "title_text": "Generalized Images for Brownian First Passage to Monomial Boundaries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/2jc77fbp8ybcd",
  "venue": "arXiv",
  "versions": []
}