{
  "abstract": "While well-established approaches exist for computing probability densities of stochastic differential equations driven by Brownian motion, computing probability densities for general stochastic differential equations driven by α-stable processes remains challenging, and few general-purpose methods are available. A major difficulty is that the corresponding Fokker--Planck equations governing the density are generally unavailable in explicit form. In this paper, we develop an efficient approach to compute probability densities for stochastic differential equations driven by α-stable processes without relying on Fokker--Planck equations or any other governing equations. The proposed approach is easy to implement and computationally efficient. Numerical examples demonstrate its effectiveness and indicate an approximately first-order convergence rate with respect to the time step.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28243",
  "author_total": 2,
  "authors": [
    {
      "name": "Yan Liu"
    },
    {
      "name": "Xu Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4v969kzp97egh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28243",
  "fulltext_url": null,
  "id": "4v969kzp97egh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28243",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7223132411",
  "pdf_url": "https://arxiv.org/pdf/2610.28243",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4v969kzp97egh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28243",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28243"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Density Evolution for Stochastic Dynamical Systems Driven by α-Stable Processes: An Equation-Free Numerical Approach",
  "title_text": "Density Evolution for Stochastic Dynamical Systems Driven by α-Stable Processes: An Equation-Free Numerical Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/4v969kzp97egh",
  "venue": "arXiv",
  "versions": []
}