Strong Convergence of Propagation of Chaos for McKean–Vlasov SDEs with Singular Interactions (Michael Röckner and collaborators)

In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular \(L^p\)-interactions as well as for the moderate interaction particle systems on the level of particle trajectories. One of the main obstacles is to establish the strong well-posedness of the SDEs for particle systems with singular interaction. To this end, we extend the results on strong well-posedness of Krylov and Röckner [Probab. Theory Related Fields, 131 (2005), pp. 154–196] to the case of mixed \(L^{\boldsymbol{p}}\)-drifts, where the heat kernel estimates play a crucial role. Moreover, when the interaction kernel is bounded measurable, we also obtain the optimal rate of strong convergence, which is partially based on Jabin and Wang’s entropy method [P.-E. Jabin and Z. Wang, J. Funct. Anal., 271 (2016), pp. 3588–3627] and Zvonkin’s transformation.

Publication:

SIAM Journal on Mathematical AnalysisVol. 56, Iss. 2 (2024)

http://dx.doi.org/10.1137/23M1556666

Author:

Zimo Hao

Fakultät für Mathematik, Universität Bielefeld, 33615, Bielefeld, Germany

School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, 430072, People’s Republic of China.

Michael Röckner

Fakultät für Mathematik, Universität Bielefeld, 33615, Bielefeld, Germany, and Academy of Mathematics and Systems Science, CAS, Beijing, China.

Email: roeckner@math.uni-bielefeld.de

Xicheng Zhang

School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China.