Work

Strong Convergence of Propagation of Chaos for McKean–Vlasov SDEs with Singular Interactions

Year: 2024

Type: article

Abstract: . In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular [Formula: see text]-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 [Formula: see text]-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.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/23m1556666

Authors: Zimo Hao, Michael Röckner, Xicheng Zhang

Institutions: Bielefeld University, Wuhan University, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, Beijing Institute of Technology

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, National Natural Science Foundation of China, National Key Research and Development Program of China

Awards: G6225716780, G6278120399, G6767698131, G7031588011, SFB 1283: Unsicherheit beherrschen und Zufall sowie Unordnung nutzen in Analysis, Stochastik und deren Anwendungen