{
  "abstract": "We study two accumulated variance functionals for stationary two-state hidden Markov or hidden semi-Markov process, observed through a single trajectory, and separate identifying these observable quantities from recovering the latent parameters behind them. For bounded durations, inverting block moments gives finite-sample upper bounds, worked out with fully explicit constants for a capped-geometric Gaussian family; on fixed interior classes, the corresponding two-point lower bounds have the same rate. On prescribed local persistence cells a long-lag estimator matches the regular and saturated regimes-though only cell by cell, with a lag built around the cell's own scale, not through any single estimator that adapts across unknown scales. Unbounded durations known only through two moments are a separate matter: no uniform exponential bound is claimed there either.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Wilson Andres Lombardo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f323fbtqgdr2c.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "f323fbtqgdr2c",
  "issns": [],
  "landing_url": "https://hal.science/hal-05736475v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-pr"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05736475/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f323fbtqgdr2c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:27Z",
      "native_id": "hal-05736475",
      "source": "hal",
      "url": "https://hal.science/hal-05736475v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-pr",
      "subfield": "probability"
    }
  ],
  "title": "Accumulated-Variance Functionals of Hidden Markov and Semi-Markov Processes: Finite-Sample Upper and Lower Bounds",
  "title_text": "Accumulated-Variance Functionals of Hidden Markov and Semi-Markov Processes: Finite-Sample Upper and Lower Bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:27Z",
  "url": "https://research.draconitic.com/paper/f323fbtqgdr2c",
  "venue": "HAL",
  "versions": []
}