Mckean-Vlasov sdes with drifts discontinuous under wasserstein distance

By Xing Huang, Feng-Yu Wang. Discrete and Continuous Dynamical Systems. Series A, 2020

57 citations recorded by the source corpus.

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 $W_0+W_\theta$ for some $\theta\ge 1$, where $W_0$ is the total variation distance and $W_\theta$ is the $L^\theta$-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.

Subfields: Finance, General Health Professions

View Paper: https://www.semanticscholar.org/paper/4098396afe0da5e104f3bbafc69e3d0eb6ea8c84

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Citations in the corpus

• Distribution dependent SDEs driven by additive fractional Brownian motion (2021, background): “This also partially answers the ongoing debate from [25, 26, 40] on whether the drift B should be taken Lipschitz continuous in themeasure argumentμw.”