{"id":"https://openalex.org/W7213601327","doi":"https://doi.org/10.48550/arxiv.2609.19769","title":"Convergence of Densities for the Euler--Maruyama Approximation of Brownian-Driven McKean--Vlasov Equations","display_name":"Convergence of Densities for the Euler--Maruyama Approximation of Brownian-Driven McKean--Vlasov Equations","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213601327","doi":"https://doi.org/10.48550/arxiv.2609.19769"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.19769","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19769","pdf_url":"https://arxiv.org/pdf/2609.19769","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.19769","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113338056","display_name":"Zhenghan Yin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yin, Zhenghan","raw_affiliation_strings":["School of Mathematics and Statistics , Huazhong University of Science and Technology , Wuhan 430074 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Huazhong University of Science and Technology , Wuhan 430074 , China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023629118","display_name":"Xu Sun","orcid":"https://orcid.org/0000-0003-1733-9353","observed_orcids":["https://orcid.org/0000-0003-1733-9353"]},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sun, Xu","raw_affiliation_strings":["School of Mathematics and Statistics , Huazhong University of Science and Technology , Wuhan 430074 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Huazhong University of Science and Technology , Wuhan 430074 , China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9794999957084656,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9794999957084656,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.006200000178068876,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.003800000064074993,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/euler-maruyama-method","display_name":"Euler-Maruyama scheme","score":0.9589999914169312},{"id":"https://openalex.org/keywords/mckean-vlasov-stochastic-differential-equations","display_name":"McKean-Vlasov stochastic differential equations","score":0.9279999732971191},{"id":"https://openalex.org/keywords/2-wasserstein-distance","display_name":"2-Wasserstein distance","score":0.824999988079071},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.5659999847412109},{"id":"https://openalex.org/keywords/numerical-approximation-of-sdes","display_name":"numerical approximation of SDEs","score":0.6470000147819519}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8565999865531921},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6710000038146973},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.6503999829292297},{"id":"https://openalex.org/C9012821","wikidata":"https://www.wikidata.org/wiki/Q2051684","display_name":"Parametrix","level":4,"score":0.6068999767303467},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5713000297546387},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.47450000047683716},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.45829999446868896},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.4496999979019165},{"id":"https://openalex.org/C206654554","wikidata":"https://www.wikidata.org/wiki/Q5374247","display_name":"Empirical measure","level":2,"score":0.4194999933242798},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.40549999475479126},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3732999861240387},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3666999936103821},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.3596000075340271},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34610000252723694},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.33000001311302185},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.3294999897480011},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.32330000400543213},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.3197999894618988},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.31859999895095825},{"id":"https://openalex.org/C65092005","wikidata":"https://www.wikidata.org/wiki/Q7885107","display_name":"Uniform limit theorem","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.28450000286102295},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.2635999917984009},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.25699999928474426},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.2556999921798706},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.25440001487731934},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C187123786","wikidata":"https://www.wikidata.org/wiki/Q4138816","display_name":"Hypoelliptic operator","level":4,"score":0.25279998779296875},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.19769","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19769","pdf_url":"https://arxiv.org/pdf/2609.19769","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.19769","doi":"https://doi.org/10.48550/arxiv.2609.19769","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.19769","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.19769","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19769","pdf_url":"https://arxiv.org/pdf/2609.19769","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213601327.pdf","grobid_xml":"https://content.openalex.org/works/W7213601327.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2027105025"],"related_works":["https://openalex.org/W4405902092","https://openalex.org/W4414908704","https://openalex.org/W7217219938","https://openalex.org/W4311638869","https://openalex.org/W4393901769","https://openalex.org/W4312279714","https://openalex.org/W2086872802","https://openalex.org/W4321505101","https://openalex.org/W7154691896","https://openalex.org/W4416640226"],"abstract_inverted_index":{"Convergence":[0],"of":[1,5,39,51,65,98,105,122],"the":[2,6,18,30,33,40,48,52,70,88,95,99,111,114,117,126,133],"transition":[3],"density":[4,37,49],"Euler-Maruyama":[7],"scheme":[8,42],"for":[9,87],"a":[10,56,82,103],"Brownian-driven":[11],"McKean-Vlasov":[12,53],"stochastic":[13],"differential":[14],"equation":[15,54,101],"is":[16,43,121],"established,":[17],"coefficients":[19],"being":[20],"uniformly":[21,76],"elliptic,":[22],"spatially":[23],"smooth,":[24],"and":[25,73,91,108,116,129],"Lipschitz":[26],"with":[27,94],"respect":[28],"to":[29,45,47],"law":[31],"in":[32,55,69,77,125],"2-Wasserstein":[34,127],"distance.":[35],"The":[36,79],"p_n":[38],"n-step":[41],"shown":[44],"converge":[46],"p":[50],"Gaussian-weighted":[57],"supremum":[58],"norm":[59],"at":[60],"rate":[61],"O(n^{-1/2}),":[62],"that":[63],"is,":[64],"order":[66,123],"one":[67],"half":[68],"step":[71],"size,":[72],"hence":[74],"also":[75],"space.":[78],"proof":[80],"develops":[81],"discrete":[83,115],"parametrix":[84,97],"(Levi-Hadamard)":[85],"expansion":[86],"Euler":[89],"chain":[90],"compares":[92],"it":[93],"continuous":[96,118],"limiting":[100],"along":[102],"hierarchy":[104],"measure-flow,":[106],"time-discretisation":[107],"lattice":[109],"corrections;":[110],"discrepancy":[112],"between":[113],"measure":[119],"flows":[120],"O(n^{-1/2})":[124],"distance":[128],"does":[130],"not":[131],"degrade":[132],"final":[134],"rate.":[135]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-19T00:00:00"}
