Abstract
In this paper, we study the averaging principle for distribution dependent stochastic differential equations with drift in localized 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”.
Acknowledgments
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.
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. https://doi.org/10.3150/23-BEJ1646
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