{
  "abstract": "Time-inconsistent stochastic control admits a natural game-theoretic interpretation in which successive decision dates are represented by different selves. In the Markovian framework of Björk-Khapko-Murgoci, the corresponding continuous-time equilibrium HJB system can be motivated by discrete subgame-perfect games, but the general discrete-to-continuous passage is not automatic. We establish a quantitative convergence theorem for a smooth uniformly elliptic class with strongly concave Hamiltonians and interior equilibrium controls, allowing control in both drift and diffusion. Using the exact sample-and-hold transition law on each time step, we construct, near a given verified continuous-time BKM weak equilibrium, a unique regular discrete Markov subgame-perfect equilibrium and prove first-order convergence of continuation objects in $C^{2+β}$ Hölder norms with mixed regularity and of policies and values uniformly. The key stability mechanism is structural: the discrete first-order condition makes the frozen differential feedback correction nilpotent. A two-norm dyadic Schauder argument, local Gaussian comparison, and spatial localization turn this cancellation into mesh-uniform block stability despite the second-order coupling caused by controlled volatility.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18376",
  "author_total": 1,
  "authors": [
    {
      "name": "Sascha Desmettre"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/836gmfxnmahe0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18376",
  "fulltext_url": null,
  "id": "836gmfxnmahe0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18376",
  "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.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7221790739",
  "pdf_url": "https://arxiv.org/pdf/2610.18376",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/836gmfxnmahe0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.18376",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18376"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Quantitative Convergence of Markov Equilibria for Time-Inconsistent Controlled Diffusions",
  "title_text": "Quantitative Convergence of Markov Equilibria for Time-Inconsistent Controlled Diffusions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/836gmfxnmahe0",
  "venue": "arXiv",
  "versions": []
}