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  "title": "Reachable noise and existence of operator-valued Wishart processes",
  "shortTitle": "Where noise can reach",
  "url": "https://evidencepress.org/releases/wishart-reachable-noise/",
  "oneLine": "Drift-reachable noise determines the candidate existence domain for operator-valued Wishart covariance processes.",
  "abstract": "This unrefereed candidate classifies continuous positive trace-class Wishart processes with deterministic initial covariance by the dimension reached by the noise under the adjoint semigroup, the initial rank outside that subspace, and continuity of a Gaussian convolution. It addresses the noninteger existence questions of Cox, Cuchiero and Khedher and isolates a precise operator-order issue in a printed sufficient condition. Established finite-dimensional results and Gaussian partition methods are explicitly credited.",
  "datePublished": "2026-09-22",
  "dateModified": "2026-09-22",
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    "Anonymous"
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    "name": "Cox–Cuchiero–Khedher (2024), Open Problems 1.2 and 1.3",
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  "keywords": [
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    "stochastic analysis",
    "operator-valued covariance",
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    "Candidate existence classification by reachable dimension, outside initial rank and Gaussian continuity.",
    "Infinite reachable dimension forces an integer parameter, even for rank-one noise.",
    "Finite reachable dimension m and outside initial rank k give a continuous parameter branch alpha ≥ m+k−1, alongside the integer/rank branch.",
    "A counterexample isolates the exact printed operator-order sufficient implication."
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    {
      "citation": "Cox, Cuchiero and Khedher (2024), Infinite-dimensional Wishart processes: equation and source open questions.",
      "url": "https://doi.org/10.1214/24-EJP1173",
      "doi": "10.1214/24-EJP1173"
    },
    {
      "citation": "Graczyk, Małecki and Mayerhofer (2018), A characterization of Wishart processes and Wishart distributions: imported positive-scale theorem.",
      "url": "https://doi.org/10.1016/j.spa.2017.07.010",
      "doi": "10.1016/j.spa.2017.07.010"
    },
    {
      "citation": "Mayerhofer (2013), On the existence of non-central Wishart distributions: prior necessary and sufficient conditions.",
      "url": "https://doi.org/10.1016/j.jmva.2012.07.010",
      "doi": "10.1016/j.jmva.2012.07.010"
    },
    {
      "citation": "Van Perlo-ten Kleij (2004), Contributions to multivariate analysis with applications in marketing: integer Gaussian partition precedent.",
      "url": "https://pure.rug.nl/ws/files/9775162/thesis.pdf",
      "doi": null
    },
    {
      "citation": "He, Karbach and Khedher (2026), Pricing options on forwards in function-valued affine stochastic volatility models, arXiv v2: application context.",
      "url": "https://arxiv.org/abs/2508.14813v2",
      "doi": "10.48550/arXiv.2508.14813"
    }
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