{
  "abstract": "We study finite-horizon mean field game systems on $\\mathbb R^d$ with common white noise and quadratic control cost. The value function is allowed to have quadratic growth, and the state space is noncompact. Under Lasry--Lions monotonicity and uniform confinement and contraction assumptions on the running and terminal costs, we first establish existence and uniqueness of strong finite-horizon equilibria. We develop a weighted analytic framework for the associated stochastic forward--backward system, based on weighted stability estimates for stochastic Fokker--Planck equations, well-posedness and regularity estimates for backward stochastic Hamilton--Jacobi--Bellman equations, and a two-sided Gronwall argument adapted to the forward--backward structure. We then construct a stationary adapted regime for the common-noise MFG dynamics. Our main long-time result is a quantitative turnpike estimate: finite-horizon equilibria converge, away from the initial and terminal layers, to this stationary regime in weighted norms, both for the population density and for the gradient of the value function. We also identify the associated ergodic constant as the averaged stationary cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Wenbin Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/43ehtw6tr6jnn.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "43ehtw6tr6jnn",
  "issns": [],
  "landing_url": "https://hal.science/hal-05783310v1",
  "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-ap"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05783310/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/43ehtw6tr6jnn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:50Z",
      "native_id": "hal-05783310",
      "source": "hal",
      "url": "https://hal.science/hal-05783310v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Long-Time Behavior of Mean Field Games on $\\mathbb{R}^d$ with Common White Noise and Quadratic Growth",
  "title_text": "Long-Time Behavior of Mean Field Games on ℝ^d with Common White Noise and Quadratic Growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:50Z",
  "url": "https://research.draconitic.com/paper/43ehtw6tr6jnn",
  "venue": "HAL",
  "versions": []
}