{"paper":{"title":"A criterion for the well-posedness of McKean-Vlasov stochastic differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Zhenxin Liu, Ziting Liu","submitted_at":"2026-07-30T11:50:49Z","abstract_excerpt":"We establish strong existence and pathwise uniqueness for McKean-Vlasov stochastic differential equations with coefficients satisfying a distribution-dependent Lyapunov condition. Under a hybrid Perron-Nagumo condition that permits a non-integrable singularity at the initial time, pathwise uniqueness holds within the class of strong solutions satisfying the corresponding Lyapunov estimate. For existence, we truncate the coefficients on nested bounded domains, construct absorbed local weak solutions, pass to a weak solution via tightness arguments, and then apply a restricted Yamada-Watanabe th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28078","kind":"arxiv","version":1},"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/2607.28078/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"}