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Mckean-Vlasov sdes with drifts discontinuous under wasserstein distance

  • * Corresponding author: Feng-Yu Wang

    * Corresponding author: Feng-Yu Wang
Supported in part by NNSFC (11771326, 11831014, 11801406, 11921001)
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  • 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 $ {\mathbb W}_0 $ or $ {\mathbb W}_0+{\mathbb W}_\theta $ for some $ \theta\ge 1 $, where $ {\mathbb W}_0 $ is the total variation distance and $ {\mathbb W}_\theta $ is the $ L^\theta $-Wasserstein distance. This improves some existing results (see for instance [13]) derived for drifts continuous in the distribution variable with respect to the Wasserstein distance.

    Mathematics Subject Classification: Primary: 60H10; Secondary: 60G44.


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