{
  "abstract": "Using the local time-space calculus of Peskir (2005) and the method developed in Mijatovic (2010), we derive a new integral representation for the backward probability associated with the first-passage time (FPT) of a diffusion process through a time-dependent barrier. We present a complete three-step numerical algorithm: first, the problem is reduced to a Volterra-type integral equation; second, its kernel is approximated by a Markov chain; finally, the resulting equation is solved using a quadrature rule. The method is implemented for several representative examples, and its convergence properties are established. An extension to double barrier problems is carried out",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.13732",
  "author_total": 3,
  "authors": [
    {
      "name": "Jerome Detemple"
    },
    {
      "name": "Yerkin Kitapbayev"
    },
    {
      "name": "Danila Shabalin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2a67gpetx8ft9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.13732",
  "fulltext_url": null,
  "id": "2a67gpetx8ft9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.13732",
  "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.CP"
    ],
    [
      "arxiv",
      "q-fin.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7203610132",
  "pdf_url": "https://arxiv.org/pdf/2608.13732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2a67gpetx8ft9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2608.13732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.13732"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On the First Hitting Time Problems for Diffusion Processes: Local Time-Space Approach",
  "title_text": "On the First Hitting Time Problems for Diffusion Processes: Local Time-Space Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/2a67gpetx8ft9",
  "venue": "arXiv",
  "versions": []
}