Theory of Probability &Its Applications, Volume 66, Issue 3, Page 469-473, January 2021.
Pathwise uniqueness for the multidimensional stochastic McKean--Vlasov equation is established under moderate regularity conditions on the drift and diffusion coefficients. Both drift and diffusion depend on the marginal measure of the solution. It is assumed that both coefficients are bounded, and, moreover, the drift is Dini-continuous in the state variable, and the diffusion satisfies the Lipschitz condition and is also continuous in time and uniformly nondegenerate. This is the classical McKean--Vlasov setting, that is, the coefficients of the equation are represented as integrals over the marginal distributions of the process.

中文翻译：

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关于多维McKean--Vlasov方程解的路径唯一性

Theory of Probability & Its Applications，第 66 卷，第 3 期，第 469-473 页，2021
年1 月。多维随机 McKean-Vlasov 方程的路径唯一性是在漂移和扩散系数的中等规律条件下建立的。漂移和扩散都取决于解决方案的边际测量。假设两个系数都是有界的，而且状态变量中的漂移是 Dini 连续的，并且扩散满足 Lipschitz 条件并且在时间上也是连续的且均匀非退化。这是经典的 McKean-Vlasov 设置，即方程的系数表示为过程边缘分布上的积分。