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

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...

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Published inJournal of theoretical probability Vol. 34; no. 3; pp. 1408 - 1425
Main Authors Ding, Xiaojie, Qiao, Huijie
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2021
Springer Nature B.V
Subjects
Approximation
Mathematical analysis
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
Vlasov equations
60H10
Euler–Maruyama approximations
Convergence rates
Stochastic McKean–Vlasov equations
Non-Lipschitz conditions
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ISSN0894-9840
1572-9230
DOI10.1007/s10959-020-01041-w

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Summary: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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ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-020-01041-w