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Euler–Maruyama Approximations for Stochastic McKean–Vlasov Equations with Non-Lipschitz Coefficients

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Abstract

In this paper, we study a type of stochastic McKean–Vlasov equations with non-Lipschitz coefficients. Firstly, by an Euler–Maruyama approximation the existence of its weak solutions is proved. Then we observe the pathwise uniqueness of its weak solutions. Finally, it is shown that the Euler–Maruyama approximation has an optimal strong convergence rate.

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Acknowledgements

The authors thank the anonymous referee for giving useful suggestions to improve this paper.

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 211189, Jiangsu, People’s Republic of China

    Xiaojie Ding & Huijie Qiao

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  1. Xiaojie Ding
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  2. Huijie Qiao
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Correspondence to Huijie Qiao.

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This work was supported by NSF of China (Nos. 11001051, 11371352) and China Scholarship Council under Grant No. 201906095034.

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Ding, X., Qiao, H. Euler–Maruyama Approximations for Stochastic McKean–Vlasov Equations with Non-Lipschitz Coefficients. J Theor Probab 34, 1408–1425 (2021). https://doi.org/10.1007/s10959-020-01041-w

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  • DOI: https://doi.org/10.1007/s10959-020-01041-w

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