{
  "abstract": "We study a linear filtering problem in which the signal process is described by a time-fractional linear stochastic differential equation driven by Brownian motion. We derive a stochastic integral equation for the conditional mean alongside a Riccati--Volterra type integral equation for the mean-square error function. As a core application, we introduce a time-fractional state-estimation framework for modelling learning trajectories in children with developmental dyscalculia.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25164",
  "author_total": 4,
  "authors": [
    {
      "name": "Olfa Draouil"
    },
    {
      "name": "Rahma Yasmina Moulay Hachemi"
    },
    {
      "name": "Bernt Øksendal"
    },
    {
      "name": "Abderrahmen Aliane"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48dkxsj42jgxa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25164",
  "fulltext_url": null,
  "id": "48dkxsj42jgxa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25164",
  "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"
    ],
    [
      "openalex",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7204491186",
  "pdf_url": "https://arxiv.org/pdf/2608.25164",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/48dkxsj42jgxa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.25164",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25164"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A time-fractional Kalman filter",
  "title_text": "A time-fractional Kalman filter",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/48dkxsj42jgxa",
  "venue": "arXiv",
  "versions": []
}