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

Author

Listed:
  • Xiaojie Ding

    (Southeast University)

  • Huijie Qiao

    (Southeast University)

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.

Suggested Citation

  • Xiaojie Ding & Huijie Qiao, 2021. "Euler–Maruyama Approximations for Stochastic McKean–Vlasov Equations with Non-Lipschitz Coefficients," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1408-1425, September.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:3:d:10.1007_s10959-020-01041-w
    DOI: 10.1007/s10959-020-01041-w
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    References listed on IDEAS

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    1. Huang, Xing & Wang, Feng-Yu, 2019. "Distribution dependent SDEs with singular coefficients," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4747-4770.
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