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

Xiaojie Ding () and Huijie Qiao ()
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Xiaojie Ding: Southeast University
Huijie Qiao: Southeast University

Journal of Theoretical Probability, 2021, vol. 34, issue 3, 1408-1425

Abstract: 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.

Keywords: Euler–Maruyama approximations; Stochastic McKean–Vlasov equations; Non-Lipschitz conditions; Convergence rates; 60H10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01041-w

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