{"paper":{"title":"Particle method and quantization-based schemes for the simulation of the McKean-Vlasov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Yating Liu","submitted_at":"2022-12-30T18:00:49Z","abstract_excerpt":"In this paper, we study three numerical schemes for the McKean-Vlasov equation \\[\\begin{cases} \\;dX_t=b(t, X_t, \\mu_t) \\, dt+\\sigma(t, X_t, \\mu_t) \\, dB_t,\\: \\\\ \\;\\forall\\, t\\in[0,T],\\;\\mu_t \\text{ is the probability distribution of }X_t, \\end{cases}\\] where $X_0$ is a known random variable. Under the assumption on the Lipschitz continuity of the coefficients $b$ and $\\sigma$, our first result proves the convergence rate of the particle method with respect to the Wasserstein distance, which extends a previous work [BT97] established in one-dimensional setting. In the second part, we present an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.14853","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/2212.14853/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"}