May 2024 Strong and weak convergence for the averaging principle of DDSDE with singular drift
Mengyu Cheng, Zimo Hao, Michael Röckner
Author Affiliations +
Bernoulli 30(2): 1586-1610 (May 2024). DOI: 10.3150/23-BEJ1646


In this paper, we study the averaging principle for distribution dependent stochastic differential equations with drift in localized Lp spaces. Using Zvonkin’s transformation and estimates for solutions to Kolmogorov equations, we prove that the solutions of the original system strongly and weakly converge to the solution of the averaged system as the time scale ε goes to zero. Moreover, we obtain rates of the strong and weak convergence that depend on p.

Funding Statement

This work is partially supported by NNSFC grants of China (Nos. 12131019, 11731009), and the German Research Foundation (DFG) through the Collaborative Research Centre(CRC) 1283/2 2021-317210226 “Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications”.


The authors sincerely thank the anonymous referee and the editor for their very careful reading of the paper and useful suggestions. The first author would like to acknowledge the warm hospitality of Bielefeld University. We would also like to thank Dr. Chengcheng Ling for many useful discussions.


Download Citation

Mengyu Cheng. Zimo Hao. Michael Röckner. "Strong and weak convergence for the averaging principle of DDSDE with singular drift." Bernoulli 30 (2) 1586 - 1610, May 2024.


Received: 1 October 2022; Published: May 2024
First available in Project Euclid: 31 January 2024

MathSciNet: MR4699565
Digital Object Identifier: 10.3150/23-BEJ1646

Keywords: averaging principle , distribution dependent SDE , heat kernel


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Vol.30 • No. 2 • May 2024
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