{
  "abstract": "We study an infinite-dimensional Skorokhod problem on the positive cone of $L_1([0,1])$, where a regulator process constrains a free càdlàg path to remain nonnegative through an oblique reflection mechanism determined by a positive linear integral operator $\\boldsymbol{F}$ on $L_1([0,1])$ with spectral radius less than $1$. This constrained process $Z$ remains in the positive cone, and the regulator $Y$ is nondecreasing with respect to the cone order and satisfies a pointwise complementarity condition, increasing only on those space-time regions where the corresponding component of $Z$ vanishes. This formulation extends the classical multidimensional Skorokhod problem on the nonnegative orthant to an infinite-dimensional setting. Under suitable assumptions on the operator $\\boldsymbol{F}$ that guarantee a dominant positive eigenfunction, we proceed through a diagonalization argument to give an alternative representation of the system in which the $L_1$ norm of the linear operator is less than 1. From this characterization, we establish existence and uniqueness of solutions for arbitrary input paths $X\\in D([0,T],L_1([0,1]))$. We further show that the associated Skorokhod map is well defined and Lipschitz continuous with respect to both the uniform and Skorokhod $J_1$ topologies. As a consequence, solutions may be obtained as limits of multidimensional Skorokhod problems, providing a constructive characterization of the infinite-dimensional reflection mechanism. These results provide a framework for the study of constrained stochastic systems with infinitely many interacting components and provide a foundation for reflected stochastic processes evolving in function spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03541",
  "author_total": 3,
  "authors": [
    {
      "name": "Louis T. Clarke"
    },
    {
      "name": "Guodong Pang"
    },
    {
      "name": "Ruoyu Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4746ng7r3290n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03541",
  "fulltext_url": null,
  "id": "4746ng7r3290n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03541",
  "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",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7220436792",
  "pdf_url": "https://arxiv.org/pdf/2610.03541",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4746ng7r3290n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03541",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03541"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "An infinite-dimensional Skorokhod problem with a diagonalization approach",
  "title_text": "An infinite-dimensional Skorokhod problem with a diagonalization approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/4746ng7r3290n",
  "venue": "arXiv",
  "versions": []
}