@article{9e7f9f22b4b9411a8aaec96beeefd148,
title = "Well-posedness of distribution dependent SDEs with singular drifts",
abstract = "Consider the following distribution dependent SDE: dXt = σt(Xt, μXt )dWt + bt(Xt, μXt )dt, where μXt stands for the distribution of Xt. In this paper for non-degenerate σ, we show the strong well-posedness of the above SDE under some integrability assumptions in the spatial variable and Lipschitz continuity in μ about b and σ. In particular, we extend the results of Krylov–R{\"o}ckner (Probab. Theory Related Fields 131 (2005) 154–196) to the distribution dependent case.",
keywords = "Distribution dependent SDEs, McKean–Vlasov system, Singular drifts, Superposition principle, Zvonkin{\textquoteright}s transformation",
author = "Michael R{\"o}ckner and Xicheng Zhang",
note = "Publisher Copyright: {\textcopyright} 2021 ISI/BS.",
year = "2021",
month = may,
doi = "10.3150/20-BEJ1268",
language = "English",
volume = "27",
pages = "1131--1158",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "Bernoulli Society for Mathematical Statistics and Probability",
number = "2",
}