Convergence rate of Euler-Maruyama scheme for McKean-Vlasov SDEs with density-dependent drift
Anh-Dung Le (TSE-R), Stéphane Villeneuve (TSE-R)
在本文中,我们研究McKean-Vlasov随机微分方程(SDE)的分布良好,其漂移点取决于边缘密度,并满足时空变量的局部可集成条件。 漂移和噪声系数假定为Lipschitz连续分布变量相对于Wasserstein指标W_p。 我们的方法是通过近似与摩尔化剂。 我们证明了解决方案的强大存在。 当p=1时获得弱和强的独特性,漂移系数为界,扩散系数为差分布。
In this paper, we study well-posedness of McKean-Vlasov stochastic differential equations (SDE) whose drift depends pointwisely on marginal density and satisfies a local integrability condition in time-space variables. The drift and noise coefficients are assumed to be Lipschitz continuous in distribution variable with respect to Wasserstein metric W_p. Our approach is by approximation with mollifiers. We prove strong existence of a solution. Weak and strong uniqueness are obtained when p=1, the...