{
  "abstract": "This paper develops a random-effects extension of the ergodic basic affine jump-diffusion (BAJD) model for a population of independent trajectories with individual unobserved jump intensities and common structural parameters. Under continuous-time observation, each intensity is estimated by the empirical jump frequency. We establish the strong consistency and stable mixed-normal limit of this estimator as the observation horizon tends to infinity. The estimated intensities are then used as pseudo-observations to construct a Bernstein-polynomial estimator of their common density. Its bias, variance, mean integrated squared error, and pointwise asymptotic normality are derived under a sequential asymptotic framework. The theory is developed for general positive jump-size distributions with finite activity and specialized to the Gamma$(k,λ)$ family, including the exponential and Erlang cases. For this family, we derive a pooled estimator of the common rate parameter and establish its consistency, asymptotic normality, and first-order conditional asymptotic independence from the individual intensity estimators. We also propose a consistent plug-in estimator of the population stationary mean. The methodology is illustrated through simulations and an empirical application to financial realized-volatility data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05567",
  "author_total": 1,
  "authors": [
    {
      "name": "Hamdi Fathallah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ypgstendy6ca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05567",
  "fulltext_url": null,
  "id": "2ypgstendy6ca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05567",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7212055055",
  "pdf_url": "https://arxiv.org/pdf/2609.05567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ypgstendy6ca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:36Z",
      "native_id": "2609.05567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05567"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Random Jump Intensities and Bernstein Density Estimation in Ergodic Basic Affine Jump-Diffusion Processes",
  "title_text": "Random Jump Intensities and Bernstein Density Estimation in Ergodic Basic Affine Jump-Diffusion Processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:36Z",
  "url": "https://research.draconitic.com/paper/2ypgstendy6ca",
  "venue": "arXiv",
  "versions": []
}