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Strong Averaging Principle for Two-Time-Scale Stochastic McKean-Vlasov Equations

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In the paper, an averaging principle problem of stochastic McKean-Vlasov equations with slow and fast time-scale is considered. Firstly, existence and uniqueness of the strong solutions of stochastic McKean-Vlasov equations with two time-scale is proved by using the Picard iteration. Secondly, we show that there exists an exponential convergence to the invariant measure for solutions of the fast equation of stochastic McKean-Vlasov equations with slow and fast time-scale. Finally, strong averaging principle for two-time-scale stochastic McKean-Vlasov equations is investigated.

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Acknowledgements

The first author is very grateful to Professor Jinqiao Duan for his encouragement and useful discussions. The authors acknowledge the support provided by key scientific research project plans of Henan province advanced universities No.21A110011, and NSFs of China No.11971154.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007, People’s Republic of China

    Jie Xu, Juanfang Liu & Yu Miao

  2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, People’s Republic of China

    Jicheng Liu

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  1. Jie Xu
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Xu, J., Liu, J., Liu, J. et al. Strong Averaging Principle for Two-Time-Scale Stochastic McKean-Vlasov Equations. Appl Math Optim 84 (Suppl 1), 837–867 (2021). https://doi.org/10.1007/s00245-021-09787-3

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