{"paper":{"title":"Existence, uniqueness and ergodicity for McKean-Vlasov SDEs under distribution-dependent Lyapunov conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jun Ma, Zhenxin Liu","submitted_at":"2023-09-11T12:23:47Z","abstract_excerpt":"In this paper, we prove the existence and uniqueness of solutions as well as ergodicity for McKean-Vlasov SDEs under Lyapunov conditions, in which the Lyapunov functions are defined on $\\mathbb R^d\\times \\mathcal P_2(\\mathbb R^d)$, i.e. the Lyapunov functions depend not only on space variable but also on distribution variable. It is reasonable and natural to consider distribution-dependent Lyapunov functions since the coefficients depends on distribution variable. We apply the martingale representation theorem and a modified Yamada-Watanabe theorem to obtain the existence and uniqueness of sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05411","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/2309.05411/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"}