论文标题
McKean-Vlasov Sdes在Wasserstein距离下不连续漂移
McKean-Vlasov SDEs with Drifts Discontinuous under Wasserstein Distance
论文作者
论文摘要
Existence and uniqueness are proved for Mckean-Vlasov type distribution dependent SDEs with singular drifts satisfying an integrability condition in space variable and the Lipschitz condition in distribution variable with respect to $W_0$ or $W_0+W_θ$ for some $θ\ge 1$, where $W_0$ is the total variation distance and $W_θ$ is the $L^θ$-Wasserstein distance.这改善了一些现有结果，其中漂移要么在空间变量中局部界定，要么在分布变量中相对于Wasserstein距离。
Existence and uniqueness are proved for Mckean-Vlasov type distribution dependent SDEs with singular drifts satisfying an integrability condition in space variable and the Lipschitz condition in distribution variable with respect to $W_0$ or $W_0+W_θ$ for some $θ\ge 1$, where $W_0$ is the total variation distance and $W_θ$ is the $L^θ$-Wasserstein distance. This improves some existing results where the drift is either locally bounded in the space variable or continuous in the distribution variable with respect to the Wasserstein distance.
