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An extra homogenized drift term containing derivative in the measure argument of the solution of the Poisson equation appears in the limit, which seems to be new and is unique for systems involving the fast distribution.<\/jats:p>","DOI":"10.1137\/22m1536856","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T04:01:18Z","timestamp":1709265678000},"page":"1495-1524","source":"Crossref","is-referenced-by-count":13,"title":["Poisson Equation on Wasserstein Space and Diffusion Approximations for Multiscale McKean\u2013Vlasov Equation"],"prefix":"10.1137","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2924-3148","authenticated-orcid":true,"given":"Yun","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, 221000, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6084-406X","authenticated-orcid":true,"given":"Fuke","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Longjie","family":"Xie","sequence":"additional","affiliation":[{"name":"Corresponding author.\u00a0School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, 221000, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,3,1]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2014-00783-9"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/16M1094117"},{"key":"ref3","first-page":"645","volume":"23","author":"Bao J.","year":"2018","journal-title":"Bernoulli"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1214\/19-AOP1410"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-010-0291-x"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2022.09.010"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1142\/S0219493723500132"},{"key":"ref8","author":"Bezemek Z. 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