{"paper":{"title":"Quantitative convergence for mean field control with common noise and degenerate idiosyncratic noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.OC","authors_text":"Alekos Cecchin, Joe Jackson, Mattia Martini, Samuel Daudin","submitted_at":"2024-09-21T08:03:16Z","abstract_excerpt":"We consider the convergence problem in the setting of mean field control with common noise and degenerate idiosyncratic noise. Our main results establish a rate of convergence of the finite-dimensional value functions $V^N$ towards the mean field value function $U$. In the case that the idiosyncratic noise is constant (but possibly degenerate), we obtain the rate $N^{-1/(d+7)}$, which is close to the conjectured optimal rate $N^{-1/d}$, and improves on the existing literature even in the non-degenerate setting. In the case that the idiosyncratic noise can be both non-constant and degenerate, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.14053","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.14053/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}